Nobody is “forced to use pronouns” at present but this stance misses the point. It looks at the harms of misgendering as a situation that doesn’t cause other inequities and harms.
For the average social interaction where you are on equal terms but can walk away being misgendered is something a lot of us hate but live with like any small annoyance. It is like stubbing your toe. Not fun but whatever it’s fine that’s just “someone being a prick”. But if deliberate misgendering is allowed to happen over a long period in a workplace setting it is not something we get to walk away from. If we have to regularly interact with that person or lose our ability to feed and house ourselves then we are forced to have mental health problems because someone essentially doesn’t like being told what to do. Having to deal with panic attacks at work because you had to be locked in a room with someone hitting every trauma trigger you have exposed to the world or else you have to find a new and maybe worse job is a barrier to participation in society.
If it’s in a medical setting where we have to balance our health outcomes knowing that if we don’t comply with the misgendering our care is impacted because a doctor holds our lives or the relief from pain in their hands. A lot of trans people become shy and don’t seek help early and often because they equate doctors visits with a sense of powerlessness and shame knowing that they can’t stand up for themselves. In that instance it’s not just “someone being a dick” you are placing someone’s complete physical wellbeing before someone’s egotistical need to be “right” about you.
If a trans person in a social club and misgendering isn’t checked by a majority it can mean that they might not have a choice on whether or not to go. The world becomes a smaller place when you have gender related trauma.
Deliberate misgendering in a professional setting isn’t just “someone showing you they are a prick” the burden always falls upon trans people disproportionately because our participation in society often forces us to compromise directly on our health and there are real traumas and weaknesses that underlie our transness. If someone was openly making rape jokes around someone you knew had sexual assault trauma you’d step in right? Why not the same for someone with gender related traumas?
What Peterson is railing against is protections for participation in regular society through professional setting misgendering cases.