'Push' autocasts; it should not
There's a general policy that when a card text includes an effect that might be detrimental to the player, that card should have a confirmation prompt instead of autocasting.
Here's the link to that
Spells: Some of them ask if you want to cast them, but others will autocast without asking first. What determines if a spell will prompt before it is cast? Answer: Spells may require prompts in situations that require a target for the effects or in situations that may be harmful to the player to cast them if this hasn’t been part of a major strategy. There may be some exceptions for this behavior, but mostly this is how the prompts behave.
It's true that you can manually deactivate cards in your hand, but you can only do this at one point during your turn, before you've already started casting cards. So, for example, if you play a Bladecoil Serpent, and that draws a bunch of cards including a Cut Your Losses, and a Push, and puts mana into them, you probably do want to cast the Cut Your Losses to gain mana (Combo players do not like it when they have to confirm casting on many cards!), but you might not want to cast the Push to destroy your own Bladecoil Serpent, particularly if Greg doesn't have any creatures in play! (Control players do not like it when cards they would rather play at the most strategic point in the game autocast instead!)
Incidentally, the same policy about 'harmful effects' includes cards which make the caster discard cards; "Time Reversal" falls into that category, and there's been a bug thread about that marked [Investigating] since March 2022.
https://forums.d3go.com/discussion/86647/time-reversal-investigating