Sounds like a diva and not a very bright one. Good coaches make their points in ways that are not interpreted. Dancing is more science than art, but a lot of dancers hate to hear that. Sounds like your current partner is one
I'd move on to save my sanity, but then again I'm a bachelor for the same reason so it's just my two cents.
I'm sorry for your situation. I myself need a very positive partner, instead of telling me what I'm doing wrong every single time....let's focus on just how to make it better. You help each other, not just one side badgering the other. Everyone practices differently, if this is as important to you as it is to me then the partnership won't last long. If you can ignore it and tune out the negativity then maybe you can make it last a year or more..but ask yourself if you can do it and if it is worth it? Of course another option is to just practice in front of a coach. Just let him observe and give his comments. Not on the quality of dancing but on the effectiveness of your practice. What do you think?
Your sanity is important. Differences aside, your "partner" seems to be on track with how she expects you to dance with her. That said this appears to be a one sided partnership. You do not mention her background in dance. Could it be her own background is extensive? and can push you to a higher level of dancing? Just a thought. You may want to have a chat per se and ask her directly if there is anything she actually likes about you as her dance partner. If you give it some time - and still feel that this is not the right partner for you - move on. There are plenty of follows - looking for a willing and able lead.
I'm not a dancer (yet), I aspire to be, although I know you should be able to take constructive criticism, it sounds like all this is is criticism. Subtle, yet important, difference. Some people have the need to make themselves feel better by making others feel bad. It seems you have found one of those. If I were you I'd move on and not waste time in this partnership. As you said, the clock is ticking. Find someone with a similar outlook (as in positive), and similar goals and you'll be better off. In life I have found the most important characteristic of a partner is that you have shared values. I believe this partner senses your consciousness of "lack of certain abilities" and is preying on them as a weak point for their own self-aggrandizement. RUN, don't walk, to a new partnership! (Just my opinion...) N