There are two main points which you are missing.

(a) Firstly, the Mishnah is not advocating marriage to a girl of three. It is simply setting the Halachic parameters of what constitutes a valid act of intercourse which will have consequent Halachic ramifications, in the same way that the next Mishnah defines the minimum age for a male as being 9 years old.

Bi'ah is one of 3 ways of contracting a valid Kidushin. Kesef and Shtar can be utilized by the girl's father to create Kidushin immediately at birth. This does not imply it is the recommended practice. It is just setting the parameter of legal validity. Bi'ah, however, which is the third way, cannot be utilized until she is three, since it would be a nullity and non-act prior to that time.

It is, however, quite clearly an unacceptable option even for an adult, as is clear from Yevamos 52a and Kidushin 12b where we find that the court would punish with lashes one who became married through Bi'ah. Moreover, Kidushin by any of the three methods is proscribed for a minor (Kidushin 41a) until she is old enough to choose her own spouse.

It is obvious therefore that the Mishnah in Nidah is merely delineating the consequences of sexual activity at the different age thresholds in accordance with the Halachic parameters.

(b) Secondly, one may not assume modern Western social and maturity levels as being universally applicable either in space or time. Even today in Oriental civilizations maturity comes much earlier. In the time of the Tanach, if the Midrash is taken literally, we hear of Rivkah marrying Yitzchak when she was three years old and of Shmuel rebuking Eli when only two years old. At the time of the Gemara in Yevamos 62b there is a strong recommendation to marry off one's children upon reaching the age of puberty. Tosfos there confirms that this applies equally to boys. This would be unthinkable in today's Western world, but at that time the Gemara positively encouraged the early marriage of boys of 12 and girls of 11.

Similarly in Kidushin 41a Tosfos make a most poignant observation about the social conditions of their time in the Franco-German region:

"The reason we have become accustomed to marry off our daughters even while still minors is because each day the Galus intensifies and if a man now has the ability to give his daughter a dowry, perhaps later he will not and his daughter will remain an Agunah forever."

We are not told whether these Kidushin were made at a very early age or whether they included Chupah too. But the message is clear: Circumstances can override the ideal where the situation so demands.

There is in fact volumes more to write about the age of marriage throughout Jewish history but the foregoing is sufficient to illustrate the point.

Kol Tuv,

Joseph Pearlman