A man is a human being with an expressed SRY gene, usually to be found on the Y chromosome. That covers literally all men, regardless of internal or external characteristics. With exceedingly few exceptions, men are born with a penis, which is part of a set of internal and external organs (primary and secondary sexual characteristics) which are part of sexual differentiation present in all mammals. The purpose of these characteristics is to allow for the procreation of the species. It is true that some men are born unable to actually procreate: that is called a defect.

The penis is used for a few different things. Urination is one of them. Ejaculation is another. These depend heavily on being connected to that set of external and internal organs, such as testes, prostate, cowpers gland, and so on and so forth. It's a complex system.

A phalloplasty is a surgical process through which an external appendage is created that is intended to appear like a penis. Given that it is not connected to the set of internal and external organs described previously, it is not capable of many of the normal functions of a penis. The absence of testes, cowper's gland, prostate, etc. means that is will never expel ejaculate, for example. It really only externally mimics a penis. It is not capable of normal erection, for example. One can, in some cases, be artificially created, but the absence of corpora cavernosa means that one cannot ever naturally occur.

What a phalloplasty creates is more appropriately termed a pseudopenis. It mimics the appearance of a penis, without being able to perform the functions thereof.

All of this, of course, in addition to the fact that no amount of phalloplasties -- or even the transplant of an actual penis, which I suspect will happen at some point -- can make up for the only thing that truly makes a man: that SRY gene.