Reading this article it says:
A firing of an enabled transition removes one token from each input place and adds one token to each output place.
Now if I have the following net, with all single arcs
After firing T1 I would expect P2 to contain 2 tokens - from P1 and P4. But the result is one token in P2. Without getting too deep into math, how it's possible to explain it?
You can make a transition that deposits two tokens at P2 if you want to (namely by having two parallel edges from T1 to P2, or if the formalism doesn't allow that, by depositing an extra token in a new dummy place from which it will immediately move to P2). But you don't have to.
Allowing a transition to destroy some tokens when it fires (or, conversely, to dispense more tokens that it takes in) provides greater flexibility when constructing a network.
It's only a mathematical model anyway -- we don't need to follow any rule of conservation of mass unless we decide to.