I see what people are trying to point out that you can't expect to beat a playstyle with one counter to it, but Baton Pass shits on its non-counters like no other style, which is why people have to resort to only one or two pokemon that can put up a fight against Baton Pass.
For example, stall breaker Gengar is too frail to set up subs against offensive teams, but it can still contribute in games against them with fast, decently powerful shadow balls and use the wisp to screw with some physical attackers. And that Unaware Clefable might not be getting its work in against a stall team who lacks powerful set up sweepers, but it can still set up a sweep with Calm Mind.
But you put the majority of the metagame up against a Baton Pass team, and all they end up doing is forcing a switch to the BP team's best counter to it, then become set-up bait.
See what happens when you just have a generic, good pokemon out, who you do not specifically equip with tools to defeat Baton Pass. Take, for example, a standard King's Shield + 3 attacks Aegislash set, the most common set on the most common pokemon on the ladder.
Suppose Aegislash is in its most favorable matchup right now, it's out against Espeon (because why would you bring it in against an unfavorable matchup). Obviously, Espeon is going to switch, because it doesn't want to take a shadow ball the the face, nor repeated shadow sneaks. You look at your options.
Shadow sneak looks nice, since you can get a solid hit on Espeon before it switches, right? Well, Espeons on Baton Pass teams are usually defensive so they can switch in to threats more easily, as Baton Pass teams can not guarantee their team members get in without a scratch each time.
4 Atk Aegislash-Blade Shadow Sneak vs. 252 HP / 252+ Def Espeon: 122-146 (36.5 - 43.7%) -- 99.7% chance to 3HKO after Leftovers recovery
If Scolipede got an Iron Defense in, you're definitely going nowhere with that one.
So you could Shadow Sneak for some chip damage, or, since the opponent will obviously switch, you can try and outplay the switch. You can try and hit the switch-in hard, but for Aegislash (and the rest of the metagame, mostly), this isn't possible; at least one of the six pokemon can take a few attacks from whatever you have out. In this case, Zapdos is your opponent's least risky option. Against any other play style besides Volt-turn, you can try and double switch, but you can't here, because Baton Pass gets to switch after you do, and they'll just bring in something else that can set up on your switch in.
So you click Shadow Sneak to hit Espeon for some chip damage, or maybe you click Shadow Ball to get as much as you can from Zapdos, but either way, Zapdos now has a free turn to use Charge as you switch to the appropriate answer to it, and you bring out a pokemon that can take on Zapdos.
If any of the other five pokemon remaining can take a few attacks from your best answer to Zapdos, you basically repeat this, only now the opponent has +1 Special Defense compared to before. With other play styles, you can force Zapdos to switch out, once again being able to get a free hit as it does so and wear the team down, but enough turns with Baton Pass, and they'll have boosted so many times your free turns on their switches mean your attack bounces off their mountain of defense boosts.
Basically, Baton Pass shits on it's non-counters way harder than the other playstyles, and the only checks to BP chains fall into 3 categories.
1. Pokemon that can stop the boosts from stacking up, like through Haze or Taunt, so you can wear down switch-ins to your pokemon in the traditional manner rather than watching your attacks deflect off +4 to both defenses behind a sub.
2. Pokemon so powerful and dangerous that none of the six opponents can both switch in and set up on it, like Landorus-I is often cited (though I have never used this one personally, I hate it), since nothing can take two hits to switch in and set up a boost.
3. Surprise attacks on pokemon that allow it to faint a member of a Baton Pass team when their guard is down, like Sturdy+Mirror Coat Avalugg.
Anything else is practically dead weight against a Baton Pass team that they use to set up.
Which means you are either putting a lot of pressure on one or two pokemon to defeat an entire team so you are very weak to misplays or even the cheap sash spore smeargle, or you're using a lot more pokemon to check Baton Pass which is obviously overcentralizing.