Ugh. I’m sorry this conversation pushes you to question your past choices regarding therapy, but also just who you are. It’s like you’ve been seeing it in a certain way, you built a solid foundation for your own well-being, you dedicate a lot of efforts to it, and someone’s comment shakes the things you’ve known for a long time. Though… it may be shaking, but it didn’t collapse, friend. This foundation of yours is strong. Because this is your life. This is your journey. This is what is meaningful to you. Which doesn’t need the approval of anyone else but you.
It sounds that this person expressed their own representation about therapy and applied some judgment on what you do and your own life. And as it seems that they’re currently facing some tough hardships in their own life, they might have a bitter way to interact. I’m not excusing anything though, just hearing that there is some context here that might have led to this kind of interaction. But on your end, even if you are willing to support and listen to them, you still deserve to be respected.
It is possible that they received your advice as being upsetting - not because of you or the subject itself, but because of how they perceive therapy. When we feel vulnerable, we want to feel like we’re actually strong and able to get better by ourselves. For many people, admitting that they need help would be a sign of weakness of character. I believed that for a long time… as I’ve always been shown that I should be able to “suck it up” and be on my own. So it becomes a matter of pride, dignity. Also why advices or personal experiences are not always welcomed, or at least not in every circumstance.
Therapy is not made for everyone, but it certainly doesn’t mean that you’d be weak for receiving counseling. I personally think that it’s a mark of strength, because it pushes you out of your comfort zone. It also requires a certain amount of humility to go to a therapist’s office. It’s a way to say: “okay, I’m not superman and I need help, I need insights, perspectives, tools, I need a space where I can be me because this society is full of limitations… etc.”. In my book, it’s far from being weak. It’s admitting that, as human beings, we are all limited in one way or another, and we need each other. And there are people out there who are trained and dedicate their life to eventually be this support.
Through your interaction, there are two different ways to perceive therapy that are clashing with each other. What is meaningful to someone may not be the same for someone else - and that is totally okay.
I guess my point is: it’s all about what is meaningful from a personal standpoint. You are the only one to be able - and to have the right - to judge the effectiveness of therapy in your life. To decide when you need it and when you don’t. No one else is living in your shoes. No one else has to judge. No one else is in your therapist’s office with you and them. And should I say, it’s always an experience in itself. At least, by going on therapy you put yourself in a position of being more able to say: I need it/I don’t need it, and evaluate that constantly. Just the very fact of giving it a try the first time was not a waste of time or money, as it allowed you to decide if it makes sense to you. Not just based on what you can hear about therapy here and there, but on your very own experience.
This comment doesn’t erase your constant efforts. For this family member, it is perceived through a lens of weakness. Lot of people think the same. Through mine, and many others, it’s perceived as a strength. Ultimately, there’s nothing wrong in believing one or another. But I hear you and I understand why this comment hurt.
Ultimately, the only thing that matters is that therapy makes sense to you and in your own life. It’s how you perceive it, what kind of value you find in it. Just because this life is yours.
As I hear this family member, it might be very scary to them to even consider therapy because of how they perceive it. They’d probably need a lot of time to even think about it. Maybe they’ll never try. But you just hit a limit with this recommendation - on this matter specifically it sounds that there’s not much you can do, at least for the moment. Except… to keep being proud of your own journey. There’s a lot of reasons to look at it and find some comfort in knowing that you made the right decisions. As you said, you tried by yourself and it didn’t work. I did too. And it had cost me more than if I decided to tame my fears and see a therapist sooner, because I had some deep/wrong misconceptions about it too.
Realizing that you need the help of someone doesn’t make you weak. Only a human being who decided to admit that they have their own limits, like everyone else. Pretending that most people are able to get their sh*t together is also a stigma. I like to remind myself sometimes that we’re all struggling at some point, we all face hardships. We just handle it differently. And the way we react to those is always valid. It’s beyond any judgment, as there’s no should or shouldn’t, but only unique lives, stories, personalities, hearts and souls. For one same event, 10 people can have 10 different reactions… and that is 100% okay. It’s unique ways to live, to react, to be. It has to be addressed in healthy ways, but it can’t be measured by knowing if those reactions make people weak or strong.
You can be proud of your decisions, your efforts and your progress. You never stopped putting one foot in front of the other.
Trying, even if not your hardest, is always enough. Just because you try, one way or another. If therapy is yours and has been yours for a long time, then so be it. And if what makes sense to you won’t be shared or approved by everyone - like anything else - then it doesn’t make it less valuable to you. 
(Long post… sorry D:)