Thesis: does the first page of Chapter 1 need to be in odd page?
This isn't just PhD theses: many books are formatted so that all chapters start on a right-hand page. Conventionally, all right-hand pages have odd numbers, and left-hand pages have even numbers. However, theses are often formatted single-sided, for the convenience of examiners, and so there would be no right/left distinction in that instance.

Another possibility is that page numbering sometimes uses Roman numerals for the "front matter" (all pages before the start of the first chapter), and then begins again with Arabic numerals for the "main matter". In this case, the first chapter will start with page 1, which is an odd number.

Your observation will not be the case for all theses, but it may hold when the institution's rules, or the software tools being used, follow these standard formatting principles.