Not sure what the context is so include the subject(s) after "Both". Also, try "their place in" or "their position in" in place of "fitting in among". Maybe add "personal" before identity.
well here's the full thing so far: As I was reading “Crossing Brooklyn Ferry,” I noticed parallels between it and the movie Finding Nemo. Both delve into issues regarding the search for one’s identity and fitting in among society while maintaining that sense of individuality.
If this is supposed to be a thesis statement, it's close.
#1. Follow Kim's suggestion in wording. You have an unparallel construction in that part of the sentence:
~ the search for one's identity
~ fitting in ...
"Unparallel" means that the two phrases don't have similar construction. You have a noun and a prepositional phrase in the first part, but a gerund phrase in the second part.
#2. A true thesis statement has your strong opinion in it. I don't see this in your sentence. It's very mild and states the obvious.
Read through ALL of the following:
Your thesis statement must include factual information (which you already have) plus your position/opinion/stance. Without your position on the topic, it isn't a true thesis statement. So think of this sentence as the angle you want to take on the topic and what you intend to prove by the end of your paper. (If your statement is simply factual, then there's nothing to prove!)
Read carefully and follow ALL directions.
This is one of the very best places I've seen online to help students write good thesis statements. It shows you sentences that aren't thesis statements and how to turn each one into real thesis statements.