I wrote an article for Jason Stellman's blog on why I believe Infant Baptism is incompatible with Reformed Theology. Since the Reformed tradition adamantly teaches Infant Baptism is a necessary and orthodox Christian teaching, if Infant Baptism is incompatible with other points of Reformed Theology, it means the Calvinist system is self-refuting and thus false.
The key question is: Does Baptism actually produce a change in the infant? For example, does the act of Baptizing, by the very act, induct an infant into the New Covenant? The answer is either Yes or No.
If the answer to that question is Yes, then on what basis do the Reformed really have for opposing the Catholic notion of Baptismal Regeneration? None that I can see. Since no text of Scripture limits the effects of Baptism to merely inducting one into the New Covenant, it would naturally imply that if Baptism does something 'automatically' to the infant, then all baptized infants receive the same gifts that the Bible says Baptism bestows. So a Yes answer is obviously unacceptable.
But if the answer to that question is No, then it means Baptism doesn't do anything to the infant, and instead is an external sign of an already existing reality. For example, throwing a birthday party is an outward sign that someone is a year older, but it doesn't make the person one year older. The problem here is that it would mean children of believing parents are automatically part of the New Covenant in virtue of their natural conception or natural birth, which seems blasphemous since basically makes Baptism superfluous and it reduces New Covenant membership to a matter of biology. This would mean a No answer is also obviously unacceptable
If both options are unacceptable, then it means Infant Baptism contradicts Reformed Theology, despite being a part of Reformed Theology, making the system inconsistent and thus self-refuting.
From my study on this matter, I think the problem is even worse, since it seems that the Reformed have equated baptism with circumcision, rather than drawing a parallel between them. And if that's the case, I see it as a variation of the Judaizer heresy, conflating life under the Mosaic Law with life in the Church. I address this more in the article linked above.