First, the dairy and the soy molecule are similar so many people who can't tolerate milk can't tolerate soy either.
Second soy is a legume and similar to the peanut molecule. People with peanut allergies can even have a severe reaction to soy. In addition, there is some suspicion that the increase of soy in our food supply may have contributed to the rising peanut allergies of children.
But, the third MOST IMPORTANT reason to not give soy milk is that it is an incredibly processed food which acts as a phytoestrogen and there is a lot of research which suggests it is unsafe for newborns and children. European countries have banned soy formulas. Weston Price has a great overview of the health implications of soy infant formula.
The most serious problem with soy formula is the presence of phytoestrogens or isoflavones. While many claims have been made about the health benefits of these estrogen-like compounds, animal studies indicate that they are powerful endocrine disrupters that alter growth patterns and cause sterility. Toxicologists estimate that an infant exclusively fed soy formula receives the estrogenic equivalent of at least five birth control pills per day. By contrast, almost no phytoestrogens have been detected in dairy-based infant formula or in human milk, even when the mother consumes soy products.