1.
Trying to weaken a Pokemon to catch it, and getting a Critical hit that instantly KO's it...
2.
Taking 20 Pokeballs to catch a Pokemon at 1 HP.
3.
Taking 20 Pokeballs to catch a Pokemon that is asleep/paralyzed and at a low HP.
4.
Losing a shiny to reason 1.
5.
Opposing Pokemon never hurting themselves while confused, never staying paralyzed, and never staying asleep.
6.
Getting Critical Hits on unimportant Pokemon.
7.
Having your final Pokemon not have neutral moves against the gym leader's Pokemon and spending 3 hours doing damage at 1 HP, only for them to use a Potion.
*I was using Nidoking against Koga's Muk, and his Muk had no attacks that either barely or didn't damage Nidoking because of its ability, and my Nidoking's only move at the time was Poison Sting, and it was not very effective...
Spent about 3 hours getting the HP low, and then Koga uses Super Potion. Eventually Muk ran out of PP and struggled to death.
As for the starter thing, I really don't care for it. I still kick their butts anyways, even pitting my own starter against theirs despite the type disadvantage.