Why does A pair with T and G with C?
There is no difference in base pairing between different kinds of organisms. Humans, animals and bacteria all share the same fundamental mechanisms as they all use DNA. Which bases can pair is determined by the chemistry of the individual bases.

The bases in DNA form the following hydrogen bonds when they are paired:




If you would try to combine other bases than the canonical Watson-Crick pairs, the hydrogen bond donors and acceptors wouldn't match. You need a donor/acceptor pair at each position.

There are different base pairs possible, but these situations don't really occur in DNA but in RNA. You can find G/U wobble base pairs and even base pairs that use different parts of the bases than the canonical base pairs, e.g. Hoogsteen base pairs.