I still don't know my exact research question but I know I don't like the ideas my advisor pushes me to work on an publish asap. What are my options? I'm three months into a fully-funded PhD programme, following on from an integrated Masters and two years in industry. I should also say upfront that after seeing more what academic research is around, I feel lukewarm at most about academia in general - which definitely contributes to any dissatisfaction I feel.

While I'm broadly interested in the subject matter of my advisor's field (I switched to work with him after my Masters), I don't feel too keen on exploring the exact research directions he pointed me towards. That being said I still haven't clarified to myself what my dream research question would be. I know what themes I'm interested in, but even though they reside in the same general field as my advisor's work, they don't match his desired themes (It's like we are both interested in cooking but I'm a vegetarian and he is keen on catering for this new hot bbq rib joint.)

So on one hand I have an advisor urging me to jump into this idea I'm not interested in, and putting pressure to find a conference to publish anything ASAP (because the idea involves a recently hot buzzword). On the other hand I'm three months into this and I still don't know what it is that I would like to research really and I'm questioning whether doing a PhD makes sense at all. Both of this sides of the problem are incredibly stressful and exert really negative effect on my mental health.

Is it abnormal / bad / embarrassing to still not know one's research question this far into the PhD programme? Would it be bad / embarrassing / disrespectful to turn down my advisor's idea even though I don't have my own to offer in exchange, and ask for more time for 'reading around'?
From an outside perspective, you are just getting started. Three months is just a warm up period. One part of me wants to advise that the doctoral study period is limited and you should do what you need to do to get through it and move on to other things. The other part wants to advise that it isn't fun to work on something you aren't interested in for a few years. Dilemma. 

But, if you intend to stay with this advisor, I suggest, pretty strongly, that you take his advice. He has more experience and a wider view than you do. It would be fine, in my view, to ask for more time to find a mutually acceptable problem to work on, but if you get push-back, I think you either need to yield or find someone else to work with. But, it may be that you can come up with an idea that he has some interest and competence in quickly enough that it works out. 

You will get the best help from your advisor, assuming you need it, if you work on a problem he is also invested in. It is possible, but harder, to work alone, but you still need his approval at the end of the day. If you can get by with minimal help and final approval, you can probably make a go of it, though it will likely take longer than if you have strong help. 

But you should look, also, to see if there is another local advisor available who has more compatible interests. You also want an advisor who will support your future career. Fighting with him won't get you that.