I feel like I'm in a wrong place, should I quit my PhD? I started a PhD program recently. I never had any doubts about the fact that I want to do a PhD and I still don't doubt it for a moment. I love working in the area of my interest, but it seems like the department I'm in isn't what I expected. Things are going very poorly for me. I'm losing my confidence, my passion, my self-esteem, my "good reputation", and I think my CV could be destroyed soon. I'm thinking about quitting the program, but I don't know how, and I don't know what the consequences could be. I very much appreciate any help or advice.

First, about the department: It's a small department at a top institution, with excellent faculty, but their approach to research and even the topics in the courses is vastly different from what I imagined. This is in the US, so the program starts without an assigned advisor and with course requirements. The courses are on the topics that my undergrad background is the weakest in, and before starting them, I was kind of happy about it, because I always knew I eventually need to learn them for my research as they are very useful tools, even though not even remotely my area of interest. But now, I can see the approach is very different from what I expected. It also seems to me that this approach represents how the professors in the department approach research problems in general.

I'm also extremely overwhelmed by the expectations. Everyone else in our very small cohort (we're only a handful of PhD student), seems to have a very strong background on the topics. They find the courses to be boring reviews, while I struggle to catch up. I was a very strong undergrad at a top institution, but my plan was to complement my undergraduate education with my graduate education, not to do the same thing again. And given the courses we have now, my strengths don't show themselves at all before I start working on my thesis (where I think I'm going to rely heavily on my undergrad background). This has shattered my confidence into pieces. I'm by far the weakest student of the cohort in the courses, and I need to work so hard to barely catch up with what others find easy and boring. 

On the other hand, soon we should choose advisors. The competition for working with the advisor I came here for seems to be unexpectedly tough this year. An unusually high number of us want to work with him, and I think I have the lowest chance for that. 

All of these combined, makes me think I chose a wrong program for my PhD. I'm starting to think about a way out, but I'm afraid of talking to the professors here about that, because our financial contract is renewed every year for a year, so I'm afraid I might get into trouble or at least, they may become overly sensitive about my performance and review my exams and assess my academic performance more strictly if I tell them about my struggles, my issues, how their expectations about my background are false, and how my expectation about the program was false. I'm also worried about my alternatives after quitting the program. How can I explain to other schools that I just chose a wrong program?! I just misunderstood what the department expects and what they do! Everyone told me since a a very long time ago, that PhD is flexible, and that a lot of people switch fields even without a proper background for their PhD. Now I entered a program that has very little flexibility, and it seems like everyone has done exactly the same topics for their undergrad!! How can I justify that I just want to start over in a different environment?!
I am so sorry that graduate school is taking such a toll on your psyche. Please believe me when I say that you are not at all alone in feeling this way, and I agree with Buffy that this largely sounds like imposter syndrome -- something that even the top academics fall trap to.

In regards to your cohort, here is my advice, regardless of whether or not you change programs: remember that there will never be an even playing field. All of you have different backgrounds, strengths, areas that need growth, goals, and research interests. There is absolutely no way that any of your cohort members check every single box. With small cohorts like yours, it is difficult not to compare (especially if your program has set up a culture of competition). However, these comparisons can be detrimental to your psyche because you are only seeing part of the picture: what your cohort members publicly present. It could very well be that you are the strongest of your cohort in areas like grant writing, interacting with certain groups of people, or even a personality that others like to be around (a major factor that might sometimes get overlooked), but you are so early in your program that only time can reveal this. Wanting to succeed in academia is half the battle; if you have this, no matter how much or how little you are bringing with you into the program, you will find your fit. There is a reason you have been selected that might not be particularly clear to you, but it was clear to the graduate admissions committee, and it helps to shift your focus from what you think you lack, onto what your strengths are/what you offer that your cohort cannot.

In my own cohort, each of us offers something different. I highly respect the intellect of all of my colleagues, and when I publicly state this, some seem surprised and have even admitted that they had not recognized x as a strength of theirs until they heard it pointed out to them. Though I cannot guarantee you will get your a-ha moment, I can guarantee that early academia makes it very easy to forget the qualities you possess that have gotten you to where you are now. There have been occasions that your cohort members have lauded you or even felt jealousy, but since this knowledge is not explicitly expressed, you are understandably feeling as if you are not "enough."

Another thing to remember - your required classes are only one small part of your PhD. You will need to learn interpersonal, research, professional, administrative, and teaching skills, many of which can be learned but the extent to which you succeed cannot. These are skills you will need no matter the school that you choose, and it is often expected that you will accumulate them on your own (with some help from your program, however it is not necessarily your program's responsibility to walk you through them). It is so very likely that despite not coming in with the same knowledge or strengths as your colleagues, you will be stronger in certain aspects of the PhD track than others, and hopefully, you will be provided an adviser who can help you assess these strengths and weaknesses with you. For me, creating an Individual Development Plan (IDP) helped tremendously.

In regards to changing programs, are there programs that allow you to enter with an adviser? If you are not provided with this adviser, is it still possible for them to be on your committee? In my program (based in the U.S.), admission is heavily contingent on the adviser you choose and committee members are just as important. At your current institution, is it the norm to meet with professors you are interested in working with, to get a better sense of what they are about? Despite the program seeming to be restrictive on academics, perhaps there are faculty members that do not feel this way and can become allies to you. Find allies within the department, let them know the surmounting stress you feel, and gain their advice. Assess whether or not you feel comfortable talking with your graduate chair (if applicable). How accessible is the person you wanted to become your advisor, and how much time do they have for their students? How many students do they have? What are they even looking for in students - is it more based on research interests, or is it on grades? I believe that no matter the discipline, it is often the prior; since you are in a PhD program, you will be there a while, and your position in the department can change for better or worse at any moment and thus should not feel set in stone. 

If all else fails, know that people do change programs to find a place with a better "fit." Finding an institution that fits your needs might take time and visiting many different institutions you had not previously considered when applying. It sounds like you have learned a lot about yourself in this process, and if you are adamant in choosing a new program, there are people in your institution that will support you and help you with this; hopefully, in your department, but at the very least, within the graduate school, academic advising, career advising, and graduate success initiatives.

Your questions regarding how to approach the situation when reaching out to schools is not easy, but it sounds like the problems you are having can be voiced in a manner that speaks about department "fit," which the right school will understand. I am unsure how you chose your current program, but speaking in person or on the phone with prospective schools and advisors is really what solidified both mine and my adviser's choice to work together. Perhaps explaining your problems with your particular program to other program's graduate coordinators might put things into perspective and allow you to see how other programs stack up on the idea of PhD flexibility. 

On your qualms about speaking up affecting your funding - is your funding contingent upon your timely progress in the program? If so, keep focusing on that while sifting out your personal feelings about the program in the background. Focus on passing those exams. Take extra initiative to get to know your department, so they can get to know you personally and your POTENTIAL rather than your current knowledge. People in your department may talk, but the extent to which they have control over your ability to stay in the program funding-wise may be minimal, and letting them to get to know you outside of hearsay will be instrumental in making a good impression - a REAL impression of you. 

Changing programs or not, you got this. I cannot emphasize enough that programs care more about your potential than how well you are doing in these classes, because academics can be taught but your willingness to learn cannot. It sounds as if you are more than willing to learn and more than capable of showing your value to your program (or to a different program that might fit your needs better). Best of luck!