Is my professor being unfair? She is sweet and helpful whenever I go to her office to ask questions about the problem sets or discuss my exam results. I have always felt like she is very picky when grading the worksheets or exams, at least in my case. For example, she would penalize a large portion of the points for a small mistake in a problem, and it really frustrated me. However, this morning, I talked to a classmate about a problem where we made similar mistakes. I lost four points out of five, and he lost half a point out of five. When I emailed to the professor about it, she told me that I am kind of “wronger” than him and that I could go and talk to her more, but that she was willing to give me one more point. I talked to her mainly because I thought it was unfair, not because I wanted that freaking point. In that problem, we had to draw a free energy diagram, and I made the energy curve between two conformations higher than both products A and B, but it should be smaller. But all the other parts of the graph are correct. For my friend, his conformation energy is higher than product B but lower than product A.

I am frustrated about it because I still think that it is unfair. I mean, if you assign a certain portion of grade to that part of the problem, only that should be taken off. For example, if you assign half a point for that portion of the graph, then only half a point should be taken off no matter how wrong that part is. However, in my case, 4 out of 5 possible points were taken off.
When lecturers mark the worksheets / assignments, they try to assess student's knowledge and understanding of the subject. Of course, they can not look inside the student's head, so they have to make judgement based on what they see. Mark schemes and rubrics are introduced for the sake of objectivity and consistency, particularly when several lecturers share the marking. However, we have to accept that no mark scheme and rubric can cover absolutely everything. There are always some distinctions between students' works which are not accounted for in the mark scheme, but still (by a lecturer's judgement) should be accounted in the grade. That's what she probably tried to explain to you when you asked. 

It is impossible to tell from the fragments you show if your work is really of the same quality as you peer's or not. We can't tell by just looking on your graphs --- something essential may be written in the comments above and below. To me it looks like these two papers are both wrong in some aspect, but I am not sure these errors are "equivalent".

You professor backed up a little by offering you an extra mark. It is hard to tell, if you really convinced you that she's been unfair, or she just don't want to spend her life arguing about it. It may well be that she deviated from the rigid set of criteria prescribed by the mark scheme, but I would not blame this on her personally. The mark scheme is not the law, in a sense that it is probably not more important than your professor's expert academic judgement. I can see a point in your frustration, but it really looks to me just as a manifestation of the complex nature of academic assessments in general, not as her bias against you.