I find it strange that you are facing this issue now. You knew the paper was submitted to a conference, and the conference trips aren't free. So you had to negotiate beforehand who's going to travel, and how to cover costs. In a way, you are in the same boat with your supervisor, and "he pays, I go" is not necessarily the default option always available.

So apply to funding agencies, or else don't go. You seem bothered by the fact that you are forced to be clear about the fact that you can't afford it. There's no shame in being a starving student.

Re the title: How is Prof. M "forcing" you to go to the conference?

@CaptainEmacs: Thank you, for giving constructive feedback. I have not discussed funding of my trip before submitting the paper. It was my mistake.

@A Simple Algorithm: Perhaps the expectation was that Prof. M would be the one attending the conference?

@rg_software at least in my field if there is a submission than is implicit the group sustains the cost. If the research is highly individual, it could be history law or something not hardware, then the professor should pay, via funds or his/her pocket. It seems absurd to expect that a student should (or even can ) manage that.

@kasa: Why can't Prof. M go by himself? 1. Prof. M is the senior author in the work; 2. probably earns a lot more than you; and 3. will likely have access to extra grant funds to fund the trip. (Unless this is one of rare instances that a conference requests the first author to present the work).

@fridaymeetssunday: I think Prof. M wants me to get an experience of the conference proceedings. Thanks for the suggestion. I will request him if he can attend.

Why is it so expensive anyway? Maybe this is part of the problem the professor is having. Is this the cheapest hotel and flight you could find (forget about the hotel the conference is in)? In my experience student travel grants don't cover nearly that amount either.

@ASimpleAlgorithm Why it costs so much is outside the scope of the question.

There's no question in your post. What is it that you want to ask us?

@fridaymeetssunday I don't think it's that rare a conference requests the first author presents?

@DavidRicherby The unusually high price may well be relevant if it explains why the professor is reluctant to pay the entirety of the sum, and suggests an avenue for solving the student's problem other than those given without this information. Perhaps the student is unaware that one can find much cheaper hotels than the venue. Or perhaps not. How might we know for sure? By my asking the above question.

@ASimpleAlgorithm The unusually high price may be relevant. But why the price is unusually high is not.

@DavidRicherby I believe my above response also addresses this nuance. Or shorter version: I assert the opposite claim that you assert, since that's all the argument you're giving in return.

@AzorAhai I would consider that unusual, I've never seen such a requirement; almost always there's a request that an author must register for the conference, and it sometimes even happens that a non-author from that institution or group presents the work. Are such requests common in some fields?

@Peteris At least in my field it's the expectation. Maybe not always required but it would be unusual to me to go up to a poster and have a non first author be there.