Wow. I'm quite concerned about your therapist's response. Yes, "feel better" or "less sad" are too vague to give a direction, but suicide would NOT help with feeling better or less sad. A dead person wouldn't feel anything in the first place. A good therapist can help you clarify your goals without jumping to mentions of suicide and without promoting myths about suicide, What if a client is in a really bad place and only realizes he or she wants to feel better or for the pain to stop? It takes work to clarify what one wants, especially when dealing with trauma, major stressors, or psychological disorders. What if a trusted therapist tells such a client that suicide would help the pain stop? I just feel very strongly about this.
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But it is very useful and necessary in therapy for the therapist to help guide you through this process. Sometimes a goal might be crystal clear, but more often than not, most of us tend to start with an unclear feeling that something needs to improve. I wonder, how is your therapist helping you clarify your therapy goals? Is she listening, asking questions, or explaining what a therapy goal might look like?