Okay, that is NOT okay. Look, I'm sorry I'm being harsh here, but you need to get some new friends STAT. It is not okay to tell someone who is asexual or aromantic that "they'll find someone eventually", and it is not okay to do something to anyone, friend or not, harmless in your eyes or not, that invalidates their identity. Just because they didn't intend to hurt you doesn't take away the fact that they HURT YOU and that they are CONTINUOUSLY HURTING YOU for no other reason than because they want to have a little fun.
Sleepy Darling, we live in a society that puts an emphasis on romantic and sexual emotions and reactions. What is considered "normal" is to be heterosexual and heteromantic, and anyone who is different is considered strange, broken, confused, or "looking for attention".
Your "friends" are invalidating your identity: because they refuse to stop shipping you with other people, it shows that they don't accept you for who you are and would rather pretend that you're something THEY think you should be instead of what you ARE; and because they act as if you're lying about being asexual, it proves that they're bad friends in the first place because they don't believe that you know more about yourself than they do and that they think they're the ones who get to make the calls about your identity.
Here's what I suggest you do:
1. Ditch your friends. I'm serious. Friends are here to support you, to care about you no matter what, and to trust and respect you. They're people who are supposed to make your life EASIER and more enjoyable, not HARDER and encourage you to doubt yourself. Find a way to meet other ace and/or aro people, be it online, through social media (ex. Tumblr, Twitter) or finding events at restaurants, bars, community centers, etc. that will make that easier. You need other people who will accept and understand you, not deny a part of your identity just because they don't like it.
2. Get a new therapist. As good as therapy can be, it's important to keep in mind that therapists are human, too, and like all humans, will be subject to outside influence. Anyone can be prejudiced, ill-informed, or have otherwise problematic ideas, even if they've been deeply educated in science. Just because EMTs are trained and have more knowledge and medical experience doesn't change the fact that African-Americans are assumed to feel less pain by many people, medical or not, and are therefore more likely to receive treatment later than non-black people. The same goes for therapy: just because you're a therapist doesn't mean you don't ascribe to the "happy is a choice" idea and end up screwing over many people with mental illnesses like depression or anxiety.
You need a better therapist that isn't misinformed and believes that asexuality isn't real and won't tell you you're "just a late bloomer". You can start looking for a therapist that will be more open to your identity by looking for a professional who frequently works with LGBTQIA+ people. If your therapist isn’t working for you for any reason, it’s okay to look for another. You have a right to be treated with respect by any mental health professional.
3. Raise your self-esteem. You're losing faith in your identity due to outside forces that aren't your own. You didn't ask to live in a society that tells you that aro ace people "don't exist" or that you're "just playing hard to get", and it's not your fault that your friends turned out to be jerks. But the good thing is, you have the ability to kick at least some of these negative factors out of your life and focus on a positive change.
Start reading up ace and aro positive stuff on the internet. Find support in the queer community. Get rid of any toxic relationships in your life. Start making goals and reward yourself when you achieve them. You can read articles on asexuality and aromance on everydayfeminism.com, get a Tumblr account and start following aro and ace positive blogs, join a Facebook group for aromantic people, scroll through Reddit for ace-positive things, etc. The list is endless.
But most importantly, you have to remember that you being an aro ace is not wrong. You are not broken or a late bloomer, you are not strange or odd, and you are not any of the negative things people have told you. Your asexuality is not a mental illness. People believe these things because they don't want their nice illusions to be destroyed. They like being able to put things in two or three boxes, and if that means saying or doing mean, hurtful, or unkind things to people that don't make sense to them or that scare them, they will. People often don't like what they don't understand. But that's not your problem, and that's something THEY need to get over. You just keep on being you, whatever you think that is or that means.