Why did the majority of the Supreme Court reject the trespass doctrine in Katz v. United States?
I assume that you are asking about the Supreme Court’s ruling in the case of Katz v. United States. I have edited your question to reflect this assumption. If this is the case about which you are asking, the Court rejected the trespass doctrine because it was too limited. The Court wanted to put forward a more expansive interpretation of the 4th Amendment.
The trespass doctrine had been enunciated in the case of Olmstead v. United States. In this case, the Court had held that there must be a physical trespass into a given place in order for the 4th Amendment to apply. In other words, under this doctrine, it was places that were protected from warrantless searches.
In Katz, the Court rejected this idea. Instead, they held that people are protected from warrantless searches. Whenever a person has a reasonable expectation of privacy, that person is protected from a warrantless search. There does not need to be any physical intrusion into the space where that person is. In Katz, this meant that it was irrelevant to ask whether there had been physical intrusion. Instead, there was only a need to ask whether Katz had been in a place where he could expect privacy.
Thus, the Supreme Court rejected the trespass doctrine because it wanted to give people more comprehensive protections under the 4th Amendment.