Why should we? Right now we need to do this kind of experiments to relieve massive pain from humans. Some tests(not all of them) can't be done without live animals.
Why should animal suffer for human? Well human have higher moral value because of higher ability of pain, emotions and cognition.
Don't get me wrong given the choice I would stop any animal cruelty if there would be alternative. As far as I know there isn't one. We can't just simply switch to some computer simulation for testing drugs instead of testing them on live animals unfortunately.
So stopping animal testing entirely doesn't seem to me to be right, but we should take a closer look at it. Be extremely careful that any harm done to animals is justified, that research being done on them really brings benefits and that we are doing best we can to relieve as much pain as it is possible.
I believe that much bigger issue eating meat, where reason why we cause huge amount of pain to animals comes mostly to , because it taste good.
There is nice overview here https://www.youtube.com/watch?v=Keqzt83KMVA.