Sorry for the bad formulated question, feel free to edit it. I will explain my question here.
I try to reflect on my abilities of proving theorems to become better at this. That is why after reading almost all proofs I wonder that I would never think about it, instead I prove until I reach the core of contradiction itself. While people deduce a little bit and return with contradiction, I take another branch of deducing and go into smaller details.
For example, I was asked to prove if A, B and C are matrices, A is invertible and AB = AC, then B = C. What my professor did is just he multiplied the equation from the left side to the inverse of A, he got identity matrices, IB = IC, so B = C. But instead of doing so, I start to think what it means to be singular (has an inverse). It means there is no zero row, for example, then it means another thing, until I show that it is impossible for B and C to be different. I hope you got the idea. What should I do to avoid such details and use what I already have? It seems like I don't see higher levels things, like I don't see the forest for the trees.
If it necessary, I can show also another example of a proof with comparisons, but it is more messy and related to vector spaces.