I never bother having intellectual arguments with people about gender any more. People are too invested in their ideas about it.
With regards to self-medding - I'm so ambivalent on that issue these days. Once I was SO set against it... thinking therapy was totally necessary before doing ANYTHING to your body because you REALLY want to be sure you are doing the right thing before you sterilise yourself and grow breasts you can never get rid of, and that the risks of potassium poisoning, clots and liver failure were really significant.
Now though... I think if you are young, don't smoke, are not overweight, and have no history of liver issues in your family, then your risk of significantly hurting yourself on starting doses of HRT are really really low in the first three months, and additionally, if you do it under supervision, then they don't actually do anything for three months after you start HRT anyway. All they do is some blood tests before you start on HRT to see what your testosterone levels are for comparison later, and to check your liver function. You can go get those tests done without asking for HRT, before you start. You can then go to a doctor after 3 months and say you already take HRT and need tests to check your levels, and then get a proper prescription (I think they are required to give you a script as a duty of care thing if you have already been taking meds for a while).
I also question the need for therapy for those who are really, really sure they are trans already, and who have support in their lives already. (If you have no support from family and friends, therapy is a good way to figure out how to set up support structures and deal with rejection).
Having said all that, I think self-medding should only be undertaken after being rejected by a doctor as a last resort - some will do the "informed consent" thing now where you just have to sign a thing to say you are aware of the effects of the meds.
And if you can't afford to see a doctor, then you need to take a serious look at how you are going to get through transition before you start. You're going to need to buy those meds, get blood tests, have facial hair removed, and you'll need to have some form of castration within 5 years of starting blockers or the risk of cancer goes up exponentially. Just starting to take HRT without any idea of how to move on from there can result in getting stuck mid-transition, and a lot of people have committed suicide from being in that position for too long, it's really stressful.