What does it mean to be "integrated enough"?

I keep hearing this from several people telling those of us, who are first-generation Americans and the offspring of immigrants, that we are not "integrated enough". As long we speak English, become educated, and contribute to American society, why should it matter what we do on our personal time? If we prefer to be around others who are culturally like us during our personal time, what is the problem? This is not a detriment to American society or illegal.