Why do Catholic priests not offer wine to members of their church during communion?

First some background

Communion is typically offered in two species: "bread" and "wine" or the body and blood of Christ. The doctrine behind communion states that receiving communion in one species as equivalent to receiving it in the other or both species. I.e. you are not better off if you only receive it one way. God is present in whichever species you are offered. And it is a personal choice to take one species or the other or both.

At mass the priest consecrates both bread and wine into the body and blood of Christ at the alter. In most churches around the world the priest consecrates sufficient quantities of wine and bread to serve to population attending mass.

Your question could imply two situations. 1 Why does the Priest normally give out the bread while someone else is distributing the wine; or 2 Why is the wine not offered to the public?

1 Why does the Priest give out the bread, while someone else gives out the wine?

Theologically there is no reason for this, although there is longstanding precedent for this. One species or the other is not more holy or more important, so the Priest could choose to serve whichever species he wants. I suspect that as all communicants take the bread and only a subset take the wine, the Priest endeavors to serve the people by giving them the most common species.

2 Why is communion only offered in one species?

That said, individual priests, parishes, or diocese sometimes decide to only offer only one species and that is normally the bread. The reasons for this are many. The recent H1N1 Swine Flu has some concerned about spreading these germs via the cup so this species has been reserved only for the priest in many parishes. Another reason is that wine (even table wine) is alcoholic and some have decided that restricting this is in the best interests of the community. Another reason is logistical, managing so many Eucharistic ministers (those who help distribute communion) is difficult (my church which provides communion in both species requires 14 helpers to serve an average mass size of 600)-when you multiply that by the number of masses each week, you realize that a parish may need almost a hundred Eucharistic ministers on the rosters.