Checks and Counters
Psychic-type Pokemon: Psychic-type Pokemon such as Xatu and Slowking resist Close Combat and threaten Hitmontop with powerful STAB moves. Xatu and Sigilyph are effectively immune to Toxic, meaning that they completely wall Hitmontop.
Flying-type Pokemon: Flying-type Pokemon are some of the biggest thorns in Hitmontop's side. Golbat is the most notable check because it is immune to Toxic and retaliates with Brave Bird. Vivillon can put Hitmontop to sleep with Sleep Powder and then can set up with Quiver Dance against it. While Braviary is not a direct switch-in to Close Combat, it does reliably KO Hitmontop with Brave Bird and can stall Close Combat out with Substitute.
Fairy-type Pokemon: Fairy-types such as Comfey and Whimsicott resist Close Combat and threaten Hitmontop with powerful STAB attacks. Mega Audino doesn't resist Close Combat, but it still threatens Hitmontop with Dazzling Gleam and can shrug off Toxic with Heal Bell.
Poison-type Pokemon: Pokemon such as Vileplume, Garbodor, and Golbat resist Hitmontop's Fighting STAB attacks and are immune to Toxic, which gives Hitmontop more trouble because it cannot do much damage to them.
Residual Damage: Hitmontop lacks reliable recovery, so Toxic poison and burns wear it down incredibly quickly. Hitmontop also hates Toxic Spikes from Garbodor, as it has to switch in in order to remove them, leaving it poisoned.