Dear Philo:

In seeking humility we do not fulfill prideful desires. It is just the opposite. In this prayer we seek to mortify all prideful desires. Perhaps I am misunderstanding your phrase, "fulfills other prideful desires".

Humans tend to seek their own ego, that is, to positively stroke the ego, to give oneself credit, to desire those things that makes our ego comfortable. The entire Litany prays for the opposite -- to be delivered from those things that bolster our ego, but even for the desire of it. For example:

The first three petitions are asking for deliverance from the desire (Deliver me, Jesus):

From the desire of being loved,
From the desire of being extolled,
From the desire of being honored,

These are negative petitions -- asking that something be taken away.

In the last section the petitions are positive, not asking for something to be taken away, but that something be given to you (Jesus, grant me the grace to desire it).

These petitions are directly correlated with the first set of intentions:

That others may be loved more than I,
That others may be esteemed more than I,
That, in the opinion of the world, others may increase and I may decrease,

Thus, we first ask for deliverance from our pride, then we ask for the grace to desire the virtue of humility so that we will not get ourselves in the pit of pride again.

Hope this helps to understand this beautiful Litany.

God Bless,
Bro. Ignatius Mary