simply becouse he is.....he can sense danger and react to it before t strkes, most of times and he is like 10 15 x more agile than ordinary man and heros.....thats why.....
ock behave.,
When he was bitten by the radio active spider his body was rewired more flexible and gave his amazing agility. Plus he just got an upgrade to all of his powers in the avengers disassembled arc.
Additionally, Spidey's muscles are extremely supple, and they can bend much further than a normal human, which makes him more flexible, which makes him more agile.