The implication of this argument is that eating is an entirely private matter in which no outside authority should have the right to interfere. Those who employ this argument often do so with the same air of indignation as those Second Amendment firearms enthusiasts who refuse to be quiet about their sacrosanct right to bear arms and who have recently gotten into the terrifying habit of brandishing semi-automatic weapons in grocery stores and restaurants. The meretricious allure of this approach is that it plays upon people's sense that their unalienable rights are somehow being infringed upon by a menacing third party who wants to impose its own agenda and values on everyone else and who has declared its right and intention to do so.

Of course, in order for a choice to be entirely personal, all those involved with or affected by it must give their consent. Punching a stranger in the face is a personal choice in the sense that it involves a decision on the part of one person to assault another, but that does not make it a “personal choice”. As the saying goes, “Your right to swing your fist ends where my nose begins.” Similarly, the “personal choice” to eat animals conveniently leaves out of the moral equation the very animals who are being exploited and slaughtered. The working assumption is that their rights and interests simply don't matter, or at least they don't matter as much as the gastronomic preferences of those who chose to eat meat, eggs, and dairy.

Another element of the equation that is universally omitted by the “personal choice” adherents is everyone else on the planet. The global animal by-product industry is responsible for environmental destruction and degradation on an enormous scale and everyone, including those of us who don't eat animals, has to live with the consequences. For instance, animal agriculture is responsible for more water pollution than any other industry in the world and the effects of that pollution are distributed equally among everyone, whether he or she contributed to the problem or not.

Here's a simple syllogism to help clarify the point:

Destroying the biosphere is not a personal choice.

The production of meat, eggs, and dairy is destroying the biosphere.

Ergo: eating meat, eggs, and dairy is not a personal choice.

Your argument is invalid.