Equal Proficiency is Required in Both Languages/

From BilingualWiki

Absolutely not.

This myth had some support with the "Threshold Hypothesis" developed by Dr. Jim Cummins, a well-known researcher in the area of childhood bilingualism and school performance. Dr. Cummins insisted that for children to enjoy the cognitive benefits of bilingualism, children's proficiency levels must be at an age-appropriate level in both languages. It should be noted, however, that Cummins' research was from the late 1970's. Later research objected to Cummin's rule on empirical and theoretical grounds.

In Carey Myles' book, "Raising Bilingual Children", he notes that subsequent sudies have shown that bilingual children who were substantially weaker in one language than the other, still achieved higher than monolingual children on various batteries of test.

The general consensus of the most linguists is that a child must be at grade level with one of the two languages. Their English, for example, isn't compromised by having less proficiency in another language.