At RCIA the question arose tonight about Mary being called ‘Mediatrix’. 

“Don’t you Catholics know that the I Timothy 2:5 says, ‘There is one mediator between God and man, the man Christ Jesus?’ ” Why do you need Mary as mediator?
Now when a Protestant throws a verse to a Catholic as a proof text that the Catholic has got something wrong there is a curious lack of logic happening. Considering the Protestant’s protestations there can only be four conclusions:
1. Catholics (if they read the Bible at all) do not know this particular verse, otherwise they would not have Mary the Mediatrix.
2. Catholics do read the Bible, and have come across this verse and deliberately ignore it, or even worse, deliberately disobey it.
3.  Catholics do read the Bible and they have read this verse, but they have a different interpretation of it
4. Catholics do read the Bible and do know this verse and accept it as God’s word, but what they mean by ‘Mary the Mediatrix’ is something different from what I think they mean.
Now the first conclusion certainly seems possible at first glance. Sadly, it is true, that most Catholics are not as immediately knowledgeable about their Bibles as most Evangelical Protestants. But we are talking about Catholic theologians here, and it is unthinkable that a theologian would be ignorant of this verse. We can therefore put that conclusion on one side.
The second conclusion we must dismiss. No sincere Christian (Catholic or otherwise) intentionally denies or disobeys the Scripture. The third conclusion is possible, but the verse in question is so clear and transparent in its meaning that it is difficult to find other interpretations than that there is one mediator between God and Man, the man Christ Jesus.
The fourth conclusion is all we are left with: Catholics must mean something different by ‘Mary Mediatrix’ than Protestants think they do. Indeed, Catholics never believe that Mary is the mediator between God and Man as her son is. 
Instead we believe she is a mediator in the way that all Christians are called to be mediators. We are all called to mediate the gospel to the world through preaching and our holy example and suffering. We are given ‘the ministry of reconciliation’ which Christ shares with us. We mediate his love to others through our lives, our prayers, our ministry and our example.
Mary does this too, and in this same say, but in a magnified dimension. She does so in this magnified dimension because of who she is. Her role from the beginning was not to be a mediator between God and man, but between her son and the world. After all, that is exactly what she did. She was the bridge between her son and the world because she conceived him, gestated him and bore him to the world, and this action and her character is therefore one of mediation in that respect.
I hope I do not labor the point, but this is but one example of how apologetics might be done. 
Protestants do not very often disagree with what Catholics believe, but they do very often disagree with what they think Catholics believe.