Computer assisted proofs are historically frowned upon because you eventually end up in a black box you have to blindly trust. Can you verify that your code is correct according to the language spec? Can you verify that your compiler is bug free and follows the spec? Can you verify that your CPU is bug free and runs the output from your compiler correctly? Can you verify that your storage medium is correct and hasn't corrupted any of your intermediate results etc. etc.

Practically people will eventually say that if your test has been run N times using M different compilers and P different computers and they all give the same answer then you're probably correct, but having a proof that humans can reason through from beginning to end makes people feel more comfortable.

That being said computer assisted proofs are becoming more and more common and mathematicians are getting more and more comfortable with them as the verification tools surrounding them keep getting better. And even if computers aren't used for the final proof they are often used for intermediate tests. For example if you're making a statement about all primes it makes sense to quickly test the first few hundred million primes to make sure there aren't any obvious counter-examples.