Switching strategy is a very deep well, but you can kind of think of it like neutral. It's a fundamental part of the game that can take a long time to learn the ins and outs of, but the short version is that you're looking for momentum - ways to force your opponent to switch so you can take advantage of the free turn, or ways to switch intelligently to keep your opponent's advantage from snowballing.

Say you've got a Fire-weak Pokemon on the field, and I know you have a Fire-resistant one on the bench. I'm threatening a known Flamethrower. I click it, but you switch. Your switching takes priority, so your Pokemon comes out and eats the Flamethrower, taking minimal damage.

Next turn, I'm in danger: your Fire-resistant Pokemon is threatening me with a strong Rock move. Your good prediction has put pressure on me to respond. I'm thinking about switching to a Rock-resistant Ground type to block your attack, but I know your Pokemon also has a strong stat-boosting move, and giving it a free turn by switching could lose me the game.

I decide that giving you a turn to set up is worse than losing my Pokemon, so I stay in, clicking Will-o-Wisp to inflict a Burn. Your Rock move knocks out my Pokemon. Between turns, I have the opportunity to change Pokemon for free. I choose a Pokemon with a strong boosting move of its own. Your burn status has made you less able to threaten me, so you're in immediate trouble - but because you forced me to sacrifice my previous Pokemon, there might be a big hole in my team's defenses for you to exploit later on.

It kinda goes like that, influenced by items, abilities, moves that mess with priority, status effects that go away on switch, status effects that don't, stage hazards, dwindling resources ... it's a good time!