Starting off my post by making it clear that Ashley11 has basically said everything I wanted to say. Regardless, I'll put things out in my own words and show why I believe Swirlix and Gligar deserve to be banned.
1) Is Gligar broken?
In my opinion, Gligar is slightly broken. It has amazing stats, movepool and typing but getting ready for it isn't mostly too hard because we have things like Misdreavus who can burn it, Murkrow's Icy Wind can either kill or cripple its speed, Scarf Pokemon with an ice move get rid of it most of the time, among other Pokemon that can take down a non-set up Gligar. The only thing that could make Gligar seem broken would be the use of Swords Dance Gligar w/Knock Off. SD Gligar with Knock Off implies all you need is 1 setup turn and you're ready to go. Scarf Pokemon can't switch into its Knock Off or else they get KOed by Gligar's amazing STAB moves and defensive Pokemon are all 2HKO because removing Eviolite makes them frail enough to be picked off by STAB.
Another reason for me to say Gligar is broken is how it can do so many different sets and there's pretty much no way of knowing the set so Gligar is basically a ticking time bomb sweeper just waiting for the right moment to come out and sweep or a huge wall that is hard to break down with Eviolite. The usage stats for January revealed the fact that Gligar has about 40% usage overall and I'm pretty sure that shouldn't sit right with anyone because when you think about it, "What can Gligar NOT do?". You need a setup Sweeper? SD w/Knock Off and STAB or SD Sub set with STAB. You need a Defog user? Offensive Defog set and Defensive Defog set. You need a pivot? U-turn Gligar's your bat! You have a weird Toxic stalling fetish? Gligar can do that as well! You need a fast Taunt user? Gligar's got this. There is literally 0 drawbacks to using Gligar because of its versatility and most of the time you can pair it up with an ice resist and that's pretty much as far as you'll need as to support and that's not even 100% necessary because honestly speaking...
232+ SpA Chinchou Ice Beam vs. 252 HP / 76 SpD Eviolite Gligar: 20-28 (76.9 - 107.6%) -- 6.3% chance to OHKO
That's cute, Chinchou, but sorry, you can't even OHKO defensive Gligar with 4x weakness attacks
If this isn't unhealthy for the metagame, I don't know what is.
1) Is Swirlix broken?
Yes, yes and yes. I'll go right to the point and say Swirlix is broken due to the versatility of its sets. In my opinion, the only sets that are borderline broken are Belly Drum and Cotton Guard + Calm Mind.
Belly Drum Swirlix is literally the most infuriating thing you'll ever find on the metagame unless you're too busy looking at Prankster ParaFusion. First off, if your team's not carrying a Meditite, it's over. But wait, like 98% of all the Pokemon, Swirlix can learn Protect! This automatically removes Meditite as a 100% counter to Swirlix because Bullet Punch only does about 60% of Swirlix's health and this turns Meditite into a shaky check to Belly Drum Swirlix. What's that? Now you say Ferroseed walls Protect BD Swirlix? Ah, don't worry, you can change up Protect and according to Game Freak's logic, cotton candy can breath fire, so Swirlix can learn Flamethrower! That's nice, isn't it? This completely removes Ferroseed from the counter list and adds Meditite back in, but then again, how would you know which moves its carrying, let alone which of the 3 movesets its carrying? We also know that Belly Drum Swirlix likes to be a sneaky little Thief and take Berry Juice from unsuspecting turtles, crabs and cyclops magnets. All 3 of these or any other Sturdy Juice user worth talking about cannot just switch in on Swirlix and do anything if Stealth Rocks are up and if you're saying Defog makes it hard for Rocks to be kept up, then sorry, losing the Berry Juice itself is basically saccing the Pokemon because of the huge number of priority users you may use to pick them off once their juice is gone. Then there's other Pokemon who may be able to take Play Rough from +6 Swirlix
+6 252+ Atk Swirlix Play Rough vs. 196 HP / 252+ Def Eviolite Slowpoke: 24-28 (85.7 - 100%) -- 6.3% chance to OHKO
(24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 28)
Yeah, so it needs a high damage roll to kill but then again, 1 hazard is all it takes for it to kill it off, since Stealth Rocks would lower 3HP from it and then... the chances of the kill increase by a lot, with only 5 damage rolls containing 24HP damage. Also, the best Slowpoke can do to Swirlix if it gets lucky is Thunder Wave and... Swirlix also learns Aromatherapy!
Now, let's pretend you played the battle thinking the opponent was going for a BD sweep but suddenly they used... Cotton Guard? Now, how is your Meditite going to kill it? I'm sorry but it can't. Cotton guard + Calm Mind is nearly unbeatable when played right without you using something obscure like HazeKrow, Wooper or had to resort to toxic stalling. Knock Off off may also be used but it uses Draining Kiss to heal so you won't get too far with that. CGCM Swirlix pretty much has all the coverage in the world having STAB Draining Kiss for recovery and having Surf, Flamethrower, Thunderbolt, Psychic and... Energy Ball? Sorry Wooper, but if people caught up with this, you wouldn't have been so useful to me. Of course, some of these moves would reduce coverage by a lot but the point is that it can use it and just run over your checks if it wants to.
There is literally nothing else to be said about this sweet, edible monster knowing it has completely different counters by switching 1 move or 2 which is stupid when you realize it's running a completely different set overall.
2) Is Swirlix / Gligar making Little Cup not fun?
Gligar's over-centralization and overuse are making Little Cup less fun, yes. Because running into a Pokemon 40% of the time is not healthy for the metagame. Swirlix... having to make a 50/50 guess that decides the battle and having to run multiple checks to it (Treecko said you need two checks to it and you would be "usually" fine? What?) limits team-building options a lot.
3) Is a combination of 1 and 2 deterring individuals from playing Little Cup?
I've seen people get bored of Gligar and Swirlix and leave. Not that many, like 2-3. Also, there's still the "FUCK GLIGAR/SWIRLIX" messages we all know and love. :D
These are my thoughts regarding Gligar and Swirlix. If someone feels I said something that is off... let me know ;3