Do they really mean half of tuition or do they mean half of the total cost of attendance (COA)?
In addition to tuition, schools have a variety of fees. Room and board are also often close to $20,000/year. Tuition at a private university might be $60,000, but total COA could be $80,000. If they are willing to pay half of tuition only, that would leave you with $50,000/year to cover by yourself. Even my state’s public universities have a pretty reasonable tuition of ~$17,000 but then R&B is another $17,000. “Half tuition” would leave you with over $25,000/year to cover on your own, which is probably unwise and maybe impossible.