A fair number of small breeds can be considered aggressive. Usually it's
a combination of being bred for toughness of temperament and being
horribly spoiled because, you know, they're little.

Most small dogs (including Chihuahuas and even dachshunds) can be
incredibly sweet, you just need to help them set parameters of what is
and is not acceptable, while not causing them to fear for their lives.
They ARE small after all.

My breeder (Min Pin) has a known biter. He's a tough little dog and he's
learned that biting gets him what he wants, so he bites. This is a dog
that I call Tony Soprano. All he needs is some chest hair and a few gold
chains.

The first time I took care of the kennel, "Tony" tried to bite me.
Instead of making a huge hairy deal out of it (which backfires big time
with tiny dogs), I just totally ignored it. I think this guy was used to
a) making a big impression on people and b) causing an uproar which c)
either resulted in getting him hurt by them or d) caused them to leave
him alone. So the bite was sort of a preemptive strike, half because he
wanted to and half because he was scared.

He was totally taken aback when I ignored him. What? No attention? No
dramatics? From that moment he decided he adored me and we're now great
friends. He's never even thought about biting me again. Go figure.