This answer may be bringing some new points only because, coming late, I've been able to draw from a number of more recent comments, trying to answer (semi-) briefly on select points. Otherwise, as the most relevant points have been discussed in great detail and length, the rest may just approximate some summarizing. But still...
How to defend plagiarism in master's thesis
Do not defend plagiarism. That is, if your wording of your question title is not just a language thing (no offense meant). Plagiarism in itself is indefensible and, as has been broadly pointed out here and elsewhere, is commonly treated as an inexcusable offense (to a point where some may even seem to stop using their brains and EQ to consider and differentiate circumstances. To be sure, neither do I mean to defend plagiarism or any motivation to plagiarize whatsoever.).
Plagiarism is not (seen as) covered by any health or state of mind issues, either (excluding recklessness, which counts as aggravating). There is simply no acknowledged health issue that is seriously believed to bring about plagiarism. (It has been discussed elsewhere on this site that some rare health issues can bring about unbelievable things (like deliberated murder incomprehensible to the victim-perpetrator), but I don't think that helps here.) So as others have said already, you had better not seem like you were trying to hide behind excuses. (The ADA thing may be valid where applicable but surely not for directly explaining plagiarism, as far as your actions are seen as that.)
Though I might contest the idea that no health issue could contribute to a course of things happening that may lead to an effect that, assessed by the rules, amounts to plagiarism -- but be very careful with that, it could count as a desperate attempt at a cover-up, so unless a seriously qualifying and qualified person (maybe at the counselling center or faculty) advised you explicitly and clearly to mention anything in that quarter (and what), or was going to mention it for you, you may be better sticking to cold facts, not including any of this.
As a corollary and general rule (though I guess that's not helping you much now, but for the classical step back and for posterity), if you are facing whatever issues that are a risk to your ability to avoid producing plagiarism, it is a very good idea to deal with them as early as possible, doing whatever is necessary. It helps to start building a habit of absolutely producing complete and sound citations from very early on during your academic progress. And rather citing "too much" than too little so in doubt you'll be erring on the side of caution.
Going from that, can you reasonably mention - only as a side point, of course not as a mainline of defense - that your habits of citing everything (which can be seen in action in all other citations you made - if these are high-quality enough to justify saying so), were insufficiently trained as this was the first thesis you had to write ever, or for a long time? Beware though, that could be self-disqualifying, too - I'm actually surprised, if I get that right from what you're writing, that you were never before required to write something that required proper citation practice.
The problem is I asked my professor that I am reading a paper and elaborating it.
Not meaning to overdo taking you literally, but that's not a problem. What's a problem (and a big one) is that you failed to expressly cite the specific paper and passage even after your supervisor expressly said you have to cite here.
27th July: ... 29th of July:
Wondering what caused the sudden change of attitude in your advisor (I really do), I'm imagining he suddenly realized that you seemed to have defied his clear order to cite and fell for the assumption this was intentional as he was so clear about it. (In this case, I'll assume this should be taken like an order -not just advice or guidance- because it is advice about really complying with the most basic rules that should be understood to be taken and complied to far earlier than only in one's graduation thesis)
About this being basic - as hinted, until the time you had to prepare a thesis in earnest, you should have trained your very gut feeling to awake you even from sleeping on Valium, and in the middle of whatever stressful work or distraction, to the slightest trace of an omission of citing any old thing, and then make you calmly and automatically and fully add whatever missing citation.
I do think it may be in your defense unless - see next paragraph that it was you who brought up the missing citation to your advisor, not vice versa. I don't dare give advice on this point in your situation but maybe somebody in the know can advise you about bringing that up in the hearing (unless your advisor will claim it's not a fact?) - it could be clear from here that there was simply nothing bad you were trying to do.
But considering that the oral defense had already happened and you did use that part of your thesis there with the citation missing, after which you brought the missing citation up to your supervisor later, it seems possible that he reacted to this by seeing it as first successfully trying to slide it by the defense audience then cover it all up by fixing it later in the paper. That would be really wrenched and sophisticated misconduct, of course. Again, I don't dare advise if and how you should react to that possibility but if there's still some time between now and your hearing, you may be able to get some advice about it.
have taken the statement of the theorems and example from that paper and tried to write all the proofs in my own word
That's a double-edged sword - it may be what (you think) you do to show that you have understood and thoroughly thought through all of it. Of course, technically it's also the same thing that the ordinary common plagiarizer would do to hide the fact that they are really just copying someone else's work.
A better approach seems to be to make it a habit to always state (if need be, ad nauseum), so-and-so explain this and that and their reasoning goes thus - recounting all of it meticulously with not ever the slightest of change (and not forgetting any of as many footnotes as may be warranted) - then add "I use this as the basics to do X, changing Y, arriving at Z via R, S and T."
(Once you do this perfectly, you may well be at liberty to summarize the work you are citing, where applicable, but always keep the distinction visible.)
Keeping the clearest visible distinction possible between your work and others' work may save you a lot of misunderstandings (and the immense effort of rewording lots of stuff that presumably has been worded well already, so in fact your rewording could not help rendering the same facts in an inferior way, which is clearly not your goal in a thesis.)
And that could be guidance to rework these parts of your thesis if you get the chance, and it seems not entirely impossible that where you are this could be seen (but you better ask the right people there) as a way to also clear up a methodical fallacy ("rewording is good") and produce a remedied version of your thesis that clearly shows your work and what is the work of others.
