a computer is a calculator in many ways.
However a calculator is NOT a computer and therefore, an abacus (calculator) is not a computer.
additionally if we are to be so pedantic as to include the abacus in the definition, is it not true that human beings created the abacus to make it easier on themselves, whereas they would normally do it with their heads?
Does it not stand to reason in such a case that the human mind would be the first calculator?
Ahh, but that is not true! many other animals have minds as well and respond to stimuli in a way that usually depends on the different stimuli. OMG! this means that animal brains support the concept of a function, which is even better then the abacus!
of course if we were to drop the pedanticism and face facts we would realize that taking advantage of the vague phrasing of the question "what was the first computer" which implicitly and quite obviously meant computers that were based on the concepts of electrical logic gates, and instead twisting it to present some misinformed argument about how pieces of wood on rods somehow constitutes the same class as the intel microprocessor is not only wrong but also insulting to the work that has been done to make the microprocessor possible.
The same pedantic argument could be used to say that a box with a hole in it is a camera.