How to deal with student with low self-awareness about health condition? Summary: Student got defensive when I suggested he might have some neurologial issue that should be checked, should I apologize or how to address the issue?
I am a PhD student advising a student midway through his master. This student has always been a very slow learner which has caused me frustration because I advise a few other students in the lab. Therefore, I don't have so much time and I feel that without my help he will fail his master.
Every protocol he makes, I have to teach him 3 times because he forgets the steps, doesn't take notes and is overall disorganized.  Our advisor has taught him how to take notes a few times but this aspect has not improved. When he tries to do the protocol by himself, he messages me asking about the steps and ultimately can not do it.
In the last 2 times we met, he was limping. The first time, he said he fell off his bicycle and on the second time he said he &quot;just fell&quot; and his legs have a lot of bruises from these falls.
The experiments we do require very steady hands, but his hands shake a lot in a way I am not sure it is normal for a young person, so he has a lot of trouble assembling the devices we make and sometimes breaks them.
Last time we met, we were going to do a new protocol. To be sure he understood, I asked him to read it and explain the steps to me. I gave him an hour to read and when I tried to check it, he couldn't explain it and asked for 3 more minutes.
I believe some activities are harder for some people and even if it is extremely difficult for someone, I should not be the person to tell them to give up. I always consider the case the person might have some personall challenges, but I can only accomodate if I know if the person  doesn't want to do a master or if the person has some disability.
Last time he failed a protocol, I asked by message if he would like to see a neurologist for these issues and he got very defensive. This makes me angry because I think he has ADHD or essential tremor or some form of anxiety which are all treatable but prevent him from doing his work and make me loose my time.
I should not diagnose him and that is why I would like him to see a professional, so I resent him not considering this option because if he has no issues, I feel like I should give up on him and let him fail, which is against my principles and the idea of &quot;giving up on someone&quot; makes me feel like a failure too.
I don't know if I should treat him as he has an undiagnosed disability or someone with the opposite of an impostor syndrome (someone who really shouldn't be doing a master but doesn't realize it).
Should I continue helping him? Give up on him?
I should not diagnose him

That's correct.  Even if you knew how to, he is not your patient.

I would like him to see a professional

Also correct.  You should tell this student they may benefit from an appointment with the disability office at your university. You can also ask that office for advice.
You should tell your supervisor about the problems with the student's performance.

Should I continue helping him?

If you have tried to help a student several times and made no progress, it is acceptable to give up.  This is particularly justified if the student refuses to follow your advice.  Depending on circumstances, you may also be able to give the student an easier research project.