The child's respect?

Can this also mean the respect of the child, as in how much the child is respected?

In English we have respect FOR someone (respect for the child.) Or if we are respected by someone we can get respect FROM them (respect from the child). I think respect OF is far too vague in English and you can't tell who respects whom. I'm not sure if this Greek sentence with the genitive means "for" or "from" but both were marked wrong. I think one ought to be correct. Thanks.