Question: My cousin, in her twenties, is sharing a flat with a young man. She says they are just friends and there is nothing intimate between them. Nonetheless, their living together somehow doesn’t seem right to me. Is it?

The situation you describe is becoming more and more common. Forty or fifty years ago, people frowned upon such a living arrangement, and few people would have adopted it, but these days it is becoming socially acceptable. What are we to make of it?
There can be different reasons why people might choose to embrace that lifestyle.
For example, someone may have rented a two-bedroom flat and now rents out the other room to someone of the opposite sex. Or two friends, workmates or classmates of the opposite sex decide to share a house or flat together.
Or a young man and woman who are engaged to marry decide to live in the same flat in order to avoid paying rent on two flats and thus save money.
Or a man and a woman are in a de facto relationship with no intention of marrying, at least for the time being.
The moral life of the people involved may thus range from those in the first cases, where there is no sexual intimacy, to the last case, where there clearly is.
Obviously, any use of sexuality outside of marriage is gravely sinful (cf CCC 2353). But is it morally acceptable to live together even when there is no sexual activity? Here there are two important considerations.
The first is the danger that, even though for the time being the man and woman have no attraction for one another and no intention of indulging in sexual activity, their very living together may give rise to the temptation to do so.
Years ago, I remember hearing of an elderly priest who had warned a younger priest about the danger of living in the same house with his housekeeper without proper separation of their living areas. He had given the wise advice that “propinquity is more dangerous than beauty”. That is, the mere fact of living in close proximity to the housekeeper, even if she was much older than he was, was more dangerous to his chastity than being in occasional contact with someone who was very beautiful.
I recall, too, the response of a wise Dominican priest who was the Master of a residential college for university students where the rule was that women were not to visit the men in their bedrooms. When some innocent students asked him, “Don’t you trust us?” he replied, ”If I were in your situation, I wouldn’t trust myself!”
Thus, an unmarried man and woman sharing a flat would ordinarily be putting themselves voluntarily without good reason into what is called an “occasion of sin”. There would be, increasingly, the likelihood that one day they might give in to the temptation to sleep together.
And there is no proportionate reason for them to be in that situation. Saving money is never a sufficient reason to put oneself in an occasion of committing a serious sin. If a couple who are engaged wish to save money, they can each share a flat with someone of the same sex, or they might choose to live at home or in some other arrangement.
What is more, living self-discipline in the area of chastity is the best preparation for the self-control needed in marriage.
The other consideration to bear in mind is scandal. That is, others knowing that a good Catholic girl is living together with a man without being married to him might be led to think that it is a perfectly acceptable arrangement and to try it themselves.
They might then be led into sin, whereas the first couple might not be committing any sin. By living together, they would thus be giving bad example and ultimately they would be held accountable before God for the sins committed by others who naively decided to imitate them.
For these reasons, it is wrong for unmarried persons to live together, even if they do not intend to engage in sexual intimacy.