It could be the other parents that are 'pushing' their two-year old toddlers, just want to ensure their children find something they're good at/know how to succeed.
I digress.
While I'm not a parent myself, it seems ludicrous to me to have toddlers in private classes. BUT, from what I understand, some cultures and countries encourage parents/guardians to find their baby's natural talents right away and get them in the best class, soonest, for opportunities they might have missed out on otherwise ... I think I heard someone tell me this is how they find (train) fifteen year old Olympic contenders and players.
Those children might be missing out on a lot.
Then again, others might say someone who's got free time in the scheduling (and letting the child determine - or, at least, have a say - how fast, how far, and how involved), means the child's not living up to his or her full potential.

It all has to do with perspectives and values. Which has no right or wrong answer.
As long as there isn't abuse or neglect, then you, baby, and spouse should be fine - encouraged in fact!

(p.s. sometimes physical discipline needs to happen. children are resilient and bounce back physically, (usually, very quickly) but they still might need that sting that gets the emotional (and social) cues/answers across.
Worried about abuse? There is a difference between a disciplining, firm, solid hand, and an abusive hand - mainly: broken bones or black-n-blue marks. discomfort that fades fairly quickly, ... well, that goes back to upbringing and culturally/socially acceptable.
Sparing the discipline is abuse.