Q:

I wanna leave my new 2-month old job. What valid reasons can I give to the interviewers?

I work as a Software Engineer (programmer), kinda in a senior level but not in paper, like I still have a senior or supervisor. 
There were multiple companies which got interested in me and they didn't seem interested at all to the reason why I'm looking for a new job even though I've been in my current job for only 2 months.
BUT there was one company that really caught me off guard when the interviewer asked me a couple of times the reason why I'm leaving my job.
Will saying I don't fit the company's culture suffice?
I know saying it's personal reasons will get me more into trouble. Like the interviewer would ask more follow-up questions. I just wanna leave my job.
REAL REASONS:

I just wanna leave my job.
I can't handle my seemingly hot-headed lead.
I just don't meet the company's expectation.
Related to #2, just hours ago, the lead, while being disappointed with me, he said that I'm very well paid. (of course he knows my rate).

p.s. Current full-time job is merely a contractual, means it's like I'm working as a freelancer but in full-time.

A:

I can't handle my seemingly hot-headed lead.

If you can phrase this appropriately, then it is a valid reason. I think the general description would be something like the job turned out to not be a good fit. "Cultural" doesn't work here, see this for reference.
It is important to gauge whether you have done your best to learn how to communicate with the lead. Two months at the job is not very much time to figure out communication and relationship. It is important because it might be a recurring problem if you don't learn how to resolve work conflicts.

A:

BUT there was one company that really caught me off guard when the interviewer asked me a couple of times the reason why I'm leaving my job. 
Will saying I don't fit the company's culture suffice?

It's not uncommon to ask why someone is leaving their company after only 2 months. It's because 2 months is not enough time to assess and make an impact on your work culture. I recommend playing up the fact that you're on a contract and you're looking for either your next contract position (as expected of contractors) or looking for more stable employment. 

