As an MP, do I have to vote for any Brexit that is put in front of me in parliament?
My duty in our representative democracy is to listen to the people and respect their views. It is also to use my own informed judgement of what is the best for my constituents and the country as a whole.
So to the question, my answer is no. If any Brexit brought to parliament is, in my judgement bad for my constituents and my country, I should not vote for it.
The Prime Minister is using a different argument. She says we have to leave the EU even if it bad for the country because the people voted for it. She suggests that the dutiful thing for MPs in light of the 2016 referendum is to vote for something that we believe is bad for this country. On the contrary, we have a duty to do the opposite.
Does this mean we defy the will of the people? No, because British democracy is a representative democracy and not just a direct democracy.
What we MPs cannot do on our own, however, in light of the referendum in 2016, is to choose to stay in the EU. We can legitimately reject any particular Brexit deal in accordance with our judgement but we cannot move from there and cancel Brexit by ourselves. This is the true meaning of the referendum result.