The reason the president may need briefings on UFOs is that the two organizations who have or had programs investigating this matter are also responsible for transferring any high priority classified information to the President's Daily Brief. Thus, either of these programs may uncover information that warrants its placement on the Daily Brief.
I will answer the question as written in the title, that is:
Why would the US President need briefings on UFOs?
The reason for this is that there seems to be no official source as to the reality of the specifc briefing you mentioned. All of the sources, including the Wikipedia page on the Advanced Aerospace Threat Identification Program (AATIP), which is the most credible public knowledge of studies relating to UFOs (officially Unidentified Aerial Phenomena), mostly reference other news articles at best and not hard documentation. That said, I will reference news articles, to establish a relevant procedural connection.
The President Receives Daily Intelligence Briefs
Every day the President is briefed from multiple sources on the most pressing matters that need his attention. This is called the President's Daily Brief. This brief is produced by the director of national intelligence, whose main role is to compile information from a coalition of 17 executive organizations for said brief:
The White House has decided that the new director of national intelligence, John D. Negroponte, will take over from CIA Director Porter J. Goss the responsibility for producing the intelligence material given to President Bush each morning, Bush Chief of Staff Andrew H. Card Jr. said yesterday.
The Navy Reports UFO Information Upon Request
Joseph Gradisher is the Deputy Chief of Naval Operations for Information Warfare, which was established by the Navy in 2014. Since it was established by the navy it is also a part of the coalition of 17 organizations under the DNI. Therefore, this part of the Navy may gather info that will eventually end up on the PDB and on the president's desk.
Gradisher has made these dual statements, which suggest that although this kind of aviation information is not available to the general public, Navy intelligence may brief other governmental staff by request.
"Military aviation safety organizations always retain reporting of hazards to aviation as privileged information in order to preserve the free and honest prioritization and discussion of safety among aircrew...no release of information to the general public is expected" (Source: LiveScience)
There have been a number of reports of unauthorized and/or unidentified aircraft entering various military-controlled ranges and designated air space in recent years. For safety and security concerns, the Navy and the USAF take these reports very seriously and investigate each and every report. As part of this effort, the Navy is updating and formalizing the process by which reports of any such suspected incursions can be m,ade to the cognizant authorities. A new message to the fleet that will detail the steps for reporting is in draft. In response to requests for information from Congressional members and staff, Navy officials have provided a series of briefings by senior Naval Intelligence officials as well as aviators who reported hazards to aviation safety." (Source: NBC News)
An Existing Intelligence Program Collects UFO Observations as Potential Threats
One of these 17 organizations is the Defense Intelligence Agency. This specific agency was associated with the AATIP studies that were released as the result of a FOIA request back in 2018:
(U//FOUO) Based on interest from your staff regarding the Defense Intelligence Agency (DIA)'s role in the Advanced Aerospace Threat and Identification Program (AATIP) please find attached a list of all products produced under the AATIP contract for DIA to publich. The purpost of AATIP was to investigate foreign advanced aerospace weapon threats from the present out to the next 40 years.
Given that the purpose of AATIP was to analyze threats and that the PDB goes over the most pressing threats of the day, it would be no surprise that something arising out of the AATIP investigation by the Defense Intelligence Agency would work its way into one of the PDBs. In addition, it is not entirely clear that AATIP ended in 2012, like it was supposed to (emphasis mine):
“The Advanced Aviation Threat Identification Program ended in the 2012 timeframe,” Pentagon spokeswoman Laura Ochoa said in an email.
“It was determined that there were other, higher priority issues that merited funding and it was in the best interest of the DoD to make a change,” she said.
But the Pentagon was less clear about whether the UFO program continues to hover somewhere in the vast universe of the U.S. defense establishment.
“The DoD takes seriously all threats and potential threats to our people, our assets, and our mission and takes action whenever credible information is developed,” Ochoa said.
Therefore it is not out of the realm of possibility that AATIP may still exist and is investigating threats that may also make their way up into the PDB.