Reviewer of PhD thesis doesn't allow me to write in the first person singular
There is an annoying truth here: What's OK in a PhD thesis and what not largely depends on the reviewers. Some people in academia have a huge inflated ego and prefer things to be done as they suggest, and the reviewer in your case is possibly among those people. You don't want to fight with them on this kind of issue.
If the reviewer has other comments that tend to create additional work without clearly improving the thesis, you may consider exchanging the reviewer.
With due respect - everyone's answers here are mostly irrelevant. The suggestions, ideas and perceptions we here on Academia.SX have on this issue are not the authoritative answer you need to get you past the review.
You need to talk to:
- Your advisor
- The administrator in charge of the "thesis phase" of PhDs in your department or your graduate school
They have some or lots of experience, respectively, with this situation, and will tell you what you should/must do when faced with such a demand from a reviewer. They may also contact the reviewer on your behalf if they believe s/he is wrong, or to explain the regulations to him/her etc.
Note that it might even be the case that you're expected to use the first person, and other reviewers will get annoyed if you switch. So you can't just cater to one person - you need to check what the default is.
There is no steadfast rule that applies across disciplines, countries, fashions, and personalities.
Do what makes your reviewers happy. Their demand is annoying, but not utterly unreasonable. More importantly, they decide over your defense and thereby your future.
This is not something worth fighting over, and certainly no reason to change supervisors.