Why is a pure virtual function initialized by 0?

The reason =0 is used is that Bjarne Stroustrup didn't think he could get another keyword, such as "pure" past the C++ community at the time the feature was being implemented. This is described in his book, The Design & Evolution of C++, section 13.2.3:

The curious =0 syntax was chosen ... because at the time I saw no chance of getting a new keyword accepted.

He also states explicitly that this need not set the vtable entry to NULL, and that doing so is not the best way of implementing pure virtual functions.

As with most "Why" questions about the design of C++, the first place to look is The Design and Evolution of C++, by Bjarne Stroustrup¹:

The curious =0 syntax was chosen over the obvious alternative of introducing a new keyword pure or abstract because at the time I saw no chance of getting a new keyword accepted. Had I suggested pure, Release 2.0 would have shipped without abstract classes. Given a choice between a nicer syntax and abstract classes, I chose abstract classes. Rather than risking delay and incurring the certain fights over pure, I used the tradition C and C++ convention of using 0 to represent "not there." The =0 syntax fits with my view that a function body is the initializer for a function also with the (simplistic, but usually adequate) view of the set of virtual functions being implemented as a vector of function pointers. [ ... ]

¹§13.2.3 Syntax

Section 9.2 of the C++ standard gives the syntax for class members. It includes this production:

pure-specifier:
    = 0

There is nothing special about the value. "= 0" is just the syntax for saying "this function is pure virtual." It has nothing to do with initialization or null pointers or the numeric value zero, although the similarity to those things may have mnemonic value.