Weird dna relationships

Statistically this can happen. It's like the long tail of a probability distribution.

The flip of the dice with the shuffliing of autosomes and recombination and the fact that you get 50% autosome contribution approx from your dad and 50% from your mother, mean that it is possible that this contribution was shuffled out.
You and a sibling will get a *different* 50% contribution from either parent.

It is unusual that it was shuffled to the degree that it is virtually undetectable in other chromosomes (but possible).

As someone said, Gedmatch could offer you an opportunity to lower the 7 centiMorgan threshold to see if there are some statistically less significant matching segments just under the thresholds which your Ancestry matching data shows for this individual.
It can happen also that people who are 6th cousins in reality might match you as 4th cousins due to statistical factors.
It is also possible that there is a statistical amplification going on with your dad's predicted relationship to this individual (unless you have a paper trail to confirm the degree of cousinship). Regardless , you would almost expect to match that person on approx 1/2 the number of matching segments as your dad does and with total/longest segments that are consistent with being 1 degree cousin distance further than your dad's predicted relationship with them.

Have you established which line this individual relates to your dad on ? His father's line or his mother's ?

--ifc

My brother & I took the Ancestry DNA test. One Great Grandmother was born in Co Galway, her husband in Co Westmeath; one grandmother was born Co Meath; three grandparents and two parents born Co Dublin. Many previous generations back as far as the 1700s born Wicklow and Dublin... yet my brother and I have very different DNA profiles on the map. My brother's DNA map doesn't include Co Galway at all whereas mine does, and the connections in the Dublin and Wicklow regions are weak. Not sure what to make of it at all!