Trans Rights are good for Men's Rights
There are many reasons to support LGBTQA+ apart from being the one yourself; if you are an empathetic person and know the struggle, or if you feel like it's a right thing to do, you can help in various ways. However, honestly, we are mostly inherently selfish beings, myself included. Just recently I had an insight on yet another purely selfish reason to support trans rights as a mostly cis man (well that's complicated, let's leave that rabbit hole aside for now).
Men face unfair treatment purely due to their gender sometimes. That happens. Common issues we're talking about here include conscription, access to medical care (mostly mental health), restricted paternity leave and access to parenting in general, far more severe punishments for the same crimes, and more.
However, most of those issues could be fixed by accepting trans rights. Let people change their gender at will. Gendered laws and restrictions will not make much sense anymore. Want to avoid conscription? Become a woman legally for the draft age. No need to change anything else, just live your life as usual. Earlier pension? Access to some necessary services? Need to care for the child? Same thing.
When people will be able to change legal gender as easily as their legal name (exceptions apply, some countries still make a big deal out of it), you can easily abuse gendered laws. And when laws can be easily and legally dismissed, they stop making sense (so they'll probably disappear or be reformed quickly).
Trans rights are human rights!