We have two events $A$ and $B$, and i'm trying to understand why :
$P(B|A)P(A)=P(A|B)P(B)=P(A\cap B)$
What i think is that if we are searching the probability that two events A and B happen simultaneously, maybe the fact that A arrives before B causes a different probability respect the case in which B arrives before A. Why am i wrong ?
@drhab pretty much explained it - you want both events to happen, this doesn't really mean that they happen simultaneously, there is no such thing as "time" when it comes to events - you can think of them as outcomes.
If you want informal explanation of the formula:
The probability of both $A$ and $B$ happening is the same as the probability of $A$ happening times the probability of $B$ happening given that $A$ happened. If you swap $A$ and $B$ you get the other identity.