Why do they say the gospels were written anonymously or by someone else after the deaths of Matthew Mark Luke and John?

[JohnD]

Jesus was born somewhere between 7 and 3 BCE. His life, death and resurrection occurred by 30 CE.

The Apostle Paul was on trial before Caesar about 66 CE. His appeal for that trial was two plus years earlier. During the meantime, Doctor Luke an associate of Paul’s investigated and produced the trial documents (the Gospel of Luke and the Acts of the Apostles).

The synoptic Gospels Matthew, Mark, and Luke are thus classified by their similarity and apparent influence on each other. But varied enough not to suggest collusion. Point being, Matthew and Mark were apparently written and established enough as credible eyewitness accounts only 30 years after the ascension of Jesus for Luke to refer to in his investigation for trial documents in 64 CE.

So, most of the eyewitnesses (writing or otherwise) were still alive at the time at least 3 of the 4 Gospels were written.

Edited August 25, 2023 by Michael37
Wording of Title amended

[Big Boy Stan Murf]

14 hours ago, JohnD said:

Why do they say the gospels were written anonymously or by someone else wrote for them after their deaths of Matthew Mark Luke and John?

The devil spreads false rumors to muddy the waters and to deceive.

[Who me]

The belief in a late date for the authorship of the gospels is very much down to the bias of the critics. 

See:- a letter to Robinson, the New Testament scholar C. H. Dodd wrote, "I should agree with you that much of the late dating is quite arbitrary, even wanton[;] the offspring not of any argument that can be presented, but rather of the critic's prejudice

and :-Bart Ehrman maintains that Robinson's early dates for the gospels, especially those for John, have not been taken up among most liberal scholars of Biblical historicity.[37] Some conservative and traditionalist scholars, however, concur with his dating of the synoptic gospels.

from wiki on the, liberal Bishop John Robinson.

https://en.m.wikipedia.org/wiki/John_Robinson_(bishop_of_Woolwich)