What on earth is that supposed to mean?
There are some pretty odious people around, whom I would have no qualms about wanting to aspire to be superior to. More to the point, if someone visits the university as a prospective student hoping to escape some sinkhole estate in the East End of London, and all it can tell them is that they can aspire to be the equal of the local gang leader, well that's not much of a future on offer...
For this homily to be true, everyone would have to be equal to everyone else. That's the only way that aspirations can be capped at equality. However, that also means that there's no point in having aspirations anyway as you're already equal to other people. The word "aspire" doesn't even make sense except in a context where some people are indeed superior in some ways to others; in particular, your new, improved self is superior to your old, pre-educated self (or if it isn't, then you're wasting your time "aspiring" to anything).
There must be some other intended reading of this, surely? "Have modest ambitions" isn't much of a rallying cry.