Logic behind masters programs admissions
You should not pay tuition to attend grad school, excepting possibly certain "professional" schools like medicine, business, law.

That is, grad programs admit a number of students for which they have funding, and have faculty/mentoring support.

Programs do not get tuition money back directly (as counter-intuitive as this might seem), but have to calibrate grad admissions to match the faculty they have ... the numbers of which are determined by essentially unrelated issues. But, approximately, programs will not admit you if they are not confident that you can succeed in their program. So you should not begrugde that judgement. And, srsly, such judgements are made with much experience.

Yes, there is the issue of prediction of success, which is an element that did not enter in undergrad studies. That is, programs do not "admit everyone" and then allow people to fail. Nor is it just a matter of "trying hard". Beyond a certain point, there is an issue of natural ability. It is true that this is highly non-trivial to understand/detect/encourage. 

Yes, there is a considerable amount of disingenuousness in how we describe graduate programs...

Perhaps reaction-comments from the OP could help refine useful answers.