I had very similar experiences when multiple professors refused to provide me recommendation letters. Including those who provided various good words about me. They gave a lot of excuses, such as they think i was a good student but since i did very bad score in masters degree and certain research entrance competitive exams so the evidence do not reflect that goodness.
(But in fact the purpose of recommendation letter is originally opposite, it is to measure the research qualities that do not reflect in an exam).
Unfortunately the recommendation letter system is often not used as it was intended for. Instead it is misused or abused. I must not generalise, but yes it is seemingly misused sometimes. Recommendation letters or forms should be used to convey the psychological insight. But unfortunately it sometimes become a battlefield of authoritative power-play, where the academia suppresses the student to be blindly obedient to the teacher to get a dazzling recommendation letter, and to a more freethinking student, the career can often be down on a "blink of eye" of professors, guides, seniors etc. So sometimes the recommendation letters tend to contain false or unknowingly wrong informations.
Also presumably many recommendation letters are not read in details. Because in an advertisement for Ph.D. admission a lot of (50, 100, 500, 1000 or more) applications arrive and a very little number of people having a versatile mentality checks those applications, and most of the applications are speedily rejected since they will fund for a very little number (usually 1 to 25) of positions. Sometimes recommendation letters written in a very mean way such as "candidate X worked in our lab for Y years, (s)he is honest, hardworking, sincere, intelligent, blah blah" as used to be in schoolday character certificate. They seemingly look for a signature and an institutional stamp. They often check for reputation and influence of the referee, and the interpersonal or inter-institutional rapport with the referee. Also the recommendation letter has the minimal role in the weightage to select the candidate, most of the recommendation process done through phone calls, in-person meetings, pannelling systems and bargaining. This is unfair, but this is real and unavoidable, it cannot yet be officially prevented, given the authority bears huge power and ego.
Also, another factor that prevents a professor from write a recommendation letter is; to writing a recommendation letter poses a risk or threat of responsibility to oneself (the referee professor) that makes them scared to write a recommendation letter say for example a the student is suffering invisible disability. Because they might think on new institute the referred student will take time to adapt and the new professors will then blame or defame the referee professor. Referral system is such a drastic way to prune out students so that if a student earns so much trust that referee take a huge risk on oneself; omly then application could be done.
In conditions your guide refuse to write the recommendation letter, ask other professors, ask more open minded teachers to give recommendation letter. even go to your earlier academia such as college and school. Make the issue open up. Explain why a recommendation letter is necessary for you. Carefully read brochure of your target institute that if they specifically mentions who can be your referee. If they does not specifically mention it, I think it is technically okay to take recommendation from your older academia such as your college teachers.
At the same time, you need to personally meet Ph. D. supervisors if it is legally allowed (in some academia it leads to disqualification as they call it "canvassing" whereas in some other places it is legal to just take an appointment and having a conversation). However it is difficult or impossible if the target institute is on another country, but still you may communicate using E-mails and video chat sessions. Explain them your specific problem with collecting recommendation letter and whether they can select you based on other available information about you.