Now, this is exasperating! Usually people who turn away from the Catholic faith have reasons. That is becoming less and less the case these days. I am sure you have encountered it in some way, even if you do not realize it. Many today do not want to think. No, I am not saying that many do not want to "think about certain things" (there are many things that we should not want to think about). What I am saying is that many people do not want to think at all. I have mentioned before that the age of rational discussion between differing parties has ended; this is now becoming more and more clear.
When you try to respond to someone's rejection of the faith and they say, "I know you believe that" or "you have no proof, that's just your opinion" or, with that stunningly brilliant piece of wisdom: "so?!", then you know that they do not want to think. You can make a perfectly cogent and compelling argument for someone like this, and he will likely just ignore it. Remarkably, those with this frame of mind will usually view themselves as brilliant; presuming that they have come up with an insurmountable argument. They believe that there is nothing you can say to them since they can just profess apathy and then proceed to ignore you.
It is this growing response that I refer to as "the shield of ignorance and the sword of arrogance". The shield of ignorance is not a true means of defense. Yet those who wield it think that they can defend themselves with it. It actually does no more than salve their consciences. They wish to live blindly, and think they have found a way to justify it. To say "I do not care" or "that is your opinion" is not a means to defend against anything. You can have no care that something is a deadly poison, but if you consume it you will still die. The fact that it is someone's opinion that Jesus Christ is Lord and Judge of all does not thereby mean that it is not true. Every truth is the same as someone's opinion. A shield of ignorance is like a shield made out of spider webs.
The sword of arrogance is also a fake weapon. Like ignorance, arrogance has no actual usefulness other than to intimidate people. Might does not make right, nor does arrogance prove one's opinions. Yet those who wish to live blindly like to proclaim loudly that they are superior (in order to hide some hated personal inferiority) so that they can continue to refuse to accept the teachings of the Church. They use this arrogance as a "sword" and seek to thrust it at us whenever we approach them with the truth. "I don't have to believe you because you are a [insert any category here]"; this is the highest form of prejudice men can fall into. Yet, because it is not a true weapon, it is comparable to being attacked with a sword that is made out of gelatin.
Those whose minds are stuck in this kind of thinking are showing that they really do not understand the Catholic faith. Most of them are rejecting a false idea of God rather than the true God merely because they refuse to think (at all) about what they are doing. It is not impossible to get through to those who think like this, but it is hard. Their "shield of ignorance and sword of arrogance" are very large in their minds because it allows them to live their lives with blinders on. This means that you have to connect with them where they are at: wallowing in their "feelings". Truth might not get through, but goodness and beauty can.
Goodness is shown in loving God and loving others. It is shown in being deeply committed to the faith in spite of what others say about it. Goodness is the working of the Holy Ghost in our lives so that we can overcome evil. Beauty is certainly physical (God has ordained a standard of what is beautiful, even if we do not yet understand it), but it is not merely physical. You can "feel" beauty, but it is most clearly recognized in what we see (whether it be a thing, or an action). Beauty is seen in the appearance of hope and an encouraging word in a time of trial. Beauty is what we call it when someone is willing to sacrifice their own desires for the sake of strangers. Show them goodness and beauty.
As we seek to bring the gospel to the lost, we have to deal with societal changes and corruptions as they come. Sometimes we are not going to be able to show the truth to someone because they refuse to open their own eyes and see it. Yet, unless the person is dead, their heart will still be open (even if they do not realize it). Appeal to them with holiness. Appeal to them by living out your life in the grace of Christ and be an example of righteousness. Righteousness and godliness are always beautiful; keep showing these things, and you will touch the hearts of those who do not know our Glorious Lord.