The Atlantic has an excellent article by Professor Eric L. Muller of the University of North Carolina School of Law about why Donald Trump probably can't pardon himself. I am not a lawyer and I know there are many lawyers here on Daily Kos, but I found this article to be clear and very understandable. The Atlantic is a subscription publication, but I'll post this link to the article for those who may want to try to read the entire article.
https://www.theatlantic.com/ideas/archive/2020/11/one-word-bars-trump-pardoning-himself/617170/
I'll give the basics of Prof. Muller's reasoning, and hope this isn't violating any rules.
To begin, Prof. Muller gives the exact language of the Constitution's Pardons clause: The President “...shall have Power to grant Reprieves and Pardons for Offenses....”. Note that this wording does not say the President can pardon; it says the President can grant pardons.
The Professor then says that when interpreting words in the Constitution, the first step is to determine if the word appears elsewhere in the Constitution and examine the context. The word grant in various forms appears several more times:
1. “legislative power herein granted ...”
2. Congress the power “to grant Letters of Marque and ...”
3. “no Title of Nobility shall be granted...”
4. “no state … shall grant Letters ...”
5. “no state … shall grant any title of Nobility.”
6. “to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions ...”
7. “… between Citizens of the same State claiming Lands under Grants of different States.”
The first six examples are of transitive verbs, where one party is transferring something to another party. A clause giving something to oneself would use a reflexive verb, and Prof. Muller gives some examples. The last example is a noun, but still referring to something having been given by one party to another.
Prof. Muller then addresses the Originalist/Textualist position by studying law dictionaries and newspapers from the late 18th century. In virtually all instances he found, the word grant was not used in the meaning of conveying something to oneself unless it read something like, well, “grant myself”.
So that's it. I've read that most legal scholars believe a President can't pardon himself. Prof. Muller's analysis makes a lot of sense to me.