Where wild minds come to rest
The above post gives you some insightful suggestions, but I would like to say that it is very hard to avoid talking about the content at all. As long as you start to argue about the difference and explain why you are having exactly MDD instead of other things, you would unintentionally/intentionally bring up contents as backups or evidence, which would end up being super confusing for the conversation.
In this case, it is not a good idea to insist on your standpoint even if you know you are right. Instead, you can try to seek a therapist directly by telling them "let's professional determine what issue I have". They are good parents, so I guess they would not reject this, and if you are able to convince your therapist, the conversation will be successful. Be careful of choosing your therapist though, some therapist are really helpful and kind, but it is possible that some would reject your claim and not caring enough to convince you entirely with their reasons.
If you are not ready for therapists, then the only way is to really just ask them for help same as the post above. Your target is to solve your own issue, and while gaining complete understanding from your parents would likely help, is not a must. In this case, you may take a step-by-step approach, and as long as they care about you, they may slowly accept your claim and start the investigation themselves, which may end up much better than you throwing everything at their face from the start.