> why would blackrock lend you their shares so that you could tank their value?
Because Blackrock commonly does whole-market index funds. They have to hold onto those shares as long as people are buying their mutual funds.
Might as well collect some interest while waiting. They wouldn't lend all their shares away: they just lend away all the shares that they expect that their mutual fund won't sell this year.
If fidelity, blackrock, vanguard etc aren't selling right now they must believe the squeeze will be real and they'll make obscene cash off it.