Guys who are complaining about this guy saying this, look at the champ pool for Assassins, Rengar, Ekko, Yi, Zed, Fizz, Akali, Kat, Nid, Kha, Talon, Shaco, Evelyn, Noc, Leblanc, Kass, and Talon. Each of these champs tend to get High HP bars sure, but they tend to have insanely high Lifesteal and Regen as well as a lot of escapes. When you see a Yi with 1 item able to pop in under turret, kill someone at full HP, and then pop out cause his Q makes him untargetable by the turret and by the time he take maybe 2 hits from turret his Q is up again and you have him dodging your skills, turret, and gets the kill.
Now most of the others are just getting too much sustain, not that they are "tanky" but they have so much sustain from skills and lifesteal that they get so hard to kill. Whereas Mages have next to no Lifesteal as everything is in their spells and they don't get Lifesteal items in their normal "meta" builds. I've seen the numbers hitting on an Akali, with just Hextech Gunblade, her auto heals her about 45-60, but her main skill, Q I think, heals her for 140-170 depending on a few things, and then there is crits. Mages don't get crits, they don't get that insane burst of healing from doing a ton of damage. The best Mages have in their normal kits are items like Rod of Ages that heals 20% of Mana Cost of a spell up to a max of 25.
Still yes this guy has a point, an Assassin should have the massive power to kill you quick, but should have the risk that they can't survive if they can't escape like the mages do.