Depends on the job
Some things are way easier to do yourself. By the time you figure out how the library works you could have done your own.
Other things like a date picker, using JQuery pays off.
Also doing things with WordPress gives you that "Me too" look unless you do your own templetes.
For server side user input validiation probably want to use a libray. Testing on your own could potentially leave you liable for client damages if your code gets cracked/hacked. Do my own JS validation client side. Its a joke, as in have to look at it as usless and test everything serverside anyway, but 99.9% of users are not malicious so it speeds up the procress most of the time.