There are some problems common to many parents:
- parents might think they have a responsibility to fix things, not to feel things with you.
- Parenting styles differ. Parents with Authoritarian parenting styles might feel that supporting you emotionally when they're also annoyed at some of the things you're doing that they disagree with is tantamount to "coddling" you, or sends mixed messages.
- when kids are suffering, it hurts the parents, too. They might feel guilty for somehow failing you. This makes it hard for them to really hear you.
- They might feel defensive, misunderstanding your desire to have a discussion as a critique of an aspect of their parenting.
- They may not want to believe there's a real problem (it scares them) so they're quick to dismiss the idea with an unhelpful response.
- They may be distracted by responsibilities that don't necessarily involve you.
- They may not understand an empathetic response is what you're looking for, because of a lack of modelling that kind of response in their family of origin or a number of other factors (e.g. a mental illness of their own.)
One approach is to write down all the responses (all of them, not just the hurtful ones) that you can remember. Evaluate them to see if they might fall into any of the above categories. If they do, categorize them, and see which are the most used methods of responding. Then preempt the "canned" responses up front. If you've removed a barrier to communication, you're more likely to make progress. (Give them credit in your calculations for the good responses.)
Easy example: if they might be preoccupied or short on time, ask them before you start a conversation if this is a good time to talk about something that might take some time. If they admit that it's not, ask them to schedule a block of time in the near future for a discussion with you. (We did this twice a week with our kids to discuss any issues we or they had with each other; we all listened, then we brainstormed.) Then write it down somewhere to remind both parties (the refrigerator works.) Make sure there are no conflicts close to that time!
Parents who think their main roll is to solve problems will take that approach first, so, early in the conversation, tell them politely and kindly what you're not looking for - any quick solutions. If they resort to a quick solution anyway, gently remind them that you are asking them for (something deeper/to be heard/taken seriously about your struggles.) Then continue to tell them about your struggles. Repeat as necessary.
If they feel guilty in some way, they might engage in blame shifting (implying that your actions, not theirs, are responsible for your feelings.) This is harder. It might help if you put them at ease before you get into the gist of your issues by telling them (if it's true) that you're grateful for everything they do for you, and give some real, concrete examples. Let them know that you take responsibility for your actions, but you want this to be about your feelings. (This preempts blame shifting. No one can truly control how they feel. People feel what they feel.) If they change the subject and blame your actions, let them finish their sentence, tell them you heard them, then remind them that you asked them for something different. Repeat as needed or it becomes obvious that it's fruitless to continue on this occasion.
Parents who haven't had empathy from their own parents will struggle with it themselves unless they made a conscious effort - before becoming parents - to avoid repeating the mistakes of their parents. The responses they make are painful. It takes a fair amount of courage to let them know that a response hurt you. It's completely fair to say (as gently as possible) that a response hurt your feelings, makes you feel put down or criticized (whatever the truth is), and that you're looking for help with your feelings, not to feel worse. ("Gently" means you're not interrupting them, you wait a moment before responding, then quietly proceed, first telling them you heard them and you understand what they're saying and why they think (what they've expressed), then owning your feelings (e.g. along the lines of "I have a problem with my self image. I feel bad about myself. When you say... I feel even worse, like I've failed again... I'm not looking for you to fix my feelings, but I am looking for some help with them.") Ask if they can just listen. Ask if they can understand that you feel, and then maybe think of something more helpful. (Be forewarned: if you try this and they perceive an accusation, the "conversation" might immediately be shut down by a more vigorously hurtful response. You can try again later when you're feeling stronger and they've calmed down.)
If parents are frightened of your pain (this is something they probably don't even know themselves; these are people who simply don't believe you have a problem, because they don't want to believe you have a problem. It's too scary to tolerate.), you probably can't have a meaningful conversation with them. The same is true if they have a mental illness themselves that prevents them from seeing things from another person's viewpoint. In that case, I would simply tell them you're struggling and would like to see if speaking with a therapist would help.
If that's out of the question, then start looking for a therapist or a kind ear in an adult yourself: your school psychologist (if there is one), a guidance counselor, a favorite teacher, or other. You can even make use of hotlines for people with serious depression or call Crisis Intervention (if it exists where you are) to ask if there's any help they can give you in finding affordable therapists. Some kindhearted therapists do pro bono (or nearly so) work. If all else fails, try a helpful self-help book (my go-to recommendation is Dr. Kabat-Zinn's Wherever You Go, There You Are. Although it sounds new-agey, it's a great resource for depression. Dr. Kabatt-Zinn refined his practice recommendations when asked to start a clinic for dealing with depression in terminally ill patients.)
You're far from alone, and I can certainly relate. If you have questions, please comment, and I'll try to deal with it with an edit. Good luck, and vow now not to repeat their mistakes with your own kids.
Edited to add: If they believe they know why you're depressed/other, and they think they know the solution, they'll keep trying to convince you of that. You need to tell them that you've heard them, and acknowledge part of their perception: "Maybe you're right that I would feel better if ("...") but I'm struggling now with my feelings, which get in the way of doing ("...") Can we focus on that for a while? On how (lonely/depressed/hopeless/alone/other) I'm feeling? Because they might think you're just not hearing what they are telling you is the problem.
Also, if they start straying and telling you what other stuff they're upset about, if's fair to tell them that they're changing the subject, or to please not pile things up on you right now, you're already overwhelmed by your feelings. It's not easy, but it's quite fair.