What defines a hard carry is their ability to perform really well late game with scaling abilities, items and with their BAT (base attack time). They won't perform well if they don't get the appropiate levels and items - but when they do get them they become stronger than other heroes with the same items and levels.
Being an agility hero is a plus since agility increases attack speed, and so with scaling abilities such as a juggernaut crit or a faceless void bash they will proc them faster, and on top of it gain extra damage with the agility as base attribute.
A crystal maiden's abilities aren't going to get better after getting maxed in levels, and her attack speed is bad. Not hard carry.
Rikimaru's backstab continues to scale after he has maxed it because it's damage is dependant on his agility, and his attack speed is above par. Hard carry. The invis is just a bonus.
Anti-mage doesn't have any spell that scale that well late game (except for his ult, but that isn't exactly spammable), but what defines him as hard carry is his smashing BAT that makes him attack really fast, his agility status and his free uninterrupted low cooldown blink dagger.
Juggernauts can play that game as well. He has that bladedance crit that continues to improve after being maxed as it is dependant on his attack damage and can even be used in his ult. Plus he has an above-average BAT. Hard carry.
He might not be the best hard-carry, most people might prefer a Spectre or Medusa over a Juggernaut with the same items, but he is none the less a hard-carry. No true or false, just hard-carry.
Yes, he has one ability that heals. So what? Luna has a supportive aura that provides damage to her allies.
Silencer and his ultimate? Supportive, yet silencer is considered hard carry because of his ability to steal int and to deliver pure damage based on it.
Yes, Juggernauts whirlwind doesn't scale with items, but neither does Ursa's Earthshock. Or Silencers Curse of the Silent. or Luna's Lucent Beam. Anti-mages Spell Shield doesn't do anything insofar as hard-carrying either. Its just more magic armor. How about Medusas Mystic Snake?
It is usually only 1 or 2 abilities that defines the hard carry.
You can believe what you want, of course, not going to take that away from you. But he is a hard-carry, albeit not one of the better ones.
Because healing is a "pure" support role. It has nothing to do with damage output, or is a reliable type of damage mitigation. The point of a hard-carry is obviously offense. Luna's aura provides a direct -damage- buff to allies. Silencer's ult is aggressive in nature, providing damage mitigation in the form of locking down opponents. Even more so, this is a great initiation spell that can turn the tide of group fights. Jugg's healing ward is simply sub-par and not something a carry would/should have.
Ursa's Earthshock isn't about damage, it's about the slow, it doesn't need to scale. I wouldn't ever pick Silencer as "the" hard carry for the team, he would be semi-carry/support. He has some short comings, which other hard carries make up for. Luna is pure offense, unlike Jugg. Anti-mage has direct damage mitigation with his Spell Shield. And as for Medusa's snake, that's an offensive ability, and the rest of her abilities compliment a carry; she has no support type abilities (her ult is meant to turn team fights and get kills).
He's a semi-carry, through and through. Name me a true carry and we'll stack them up against Jugg side by side and see how he does.
his healing help him mitigate damage, and except his spin, ALL of his other skills scale well with stat: healing ward heals by percent of max HP, crit by damage, and omnislash by damage and attack speed. He is a carry, maybe not hard, but definitely not semi