Water and earth
This is the compatible pair of elements in the usual scheme, and the reason is straightforward. Earth contains water and gives it a shape, while water keeps earth from setting hard. Cancer softens Capricorn's severity and Capricorn gives Cancer's care somewhere reliable to sit.
The failure mode is equally straightforward. Earth that takes on too much water becomes unable to hold anything, and water held too tightly stops moving. Cancer floods and Capricorn shuts down, and each blames the other for a reaction it caused.
Two cardinal signs
Both initiate. Neither waits. That means the pairing gets things done and also that there are two people trying to set the direction at once, which is a different problem from apathy and just as durable.
Opposition between cardinal signs tends to be conducted as a series of competing plans rather than as a shouting match. Each keeps proposing, neither concedes the frame, and the household ends up with two schedules that do not acknowledge each other.
The Moon and Saturn
Cancer belongs to the Moon and Capricorn to Saturn, which is about as wide a temperamental gap as the rulerships offer. The Moon changes sign every couple of days; Saturn takes years. One responds to the mood of the week and the other to the shape of the decade.
That difference in time signature is the pairing's actual subject. Where the Moon sits in the Capricorn chart, and how Saturn is placed in the Cancer chart, decides whether the two can hear each other's timescale at all.
Where it grinds
Emotional labour, and who is deemed to be doing it. Cancer notices what everyone needs and keeps supplying it; Capricorn notices what the household owes and keeps paying it. Each considers its own contribution the invisible one.
The second grind is coldness under stress. Capricorn withdraws into work when something is wrong, which Cancer reads as abandonment at the exact moment it can least tolerate it. Capricorn genuinely does not see the reading, and repetition does not make it obvious.
Why sun signs cannot settle this
An opposite-sign pairing sounds decisive and is not. Sun signs sort everyone alive into twelve categories, and a category that size predicts a tendency rather than a person, so a page like this cannot be describing anybody exactly.
What refines it is the Moon for domestic need, Venus for how affection is given and recognised, and Mars for the conduct of arguments. Comparing those across two real charts is the only version of this question with a specific answer.
Questions people ask about this
Are opposite signs compatible?
Opposition puts each in charge of what the other neglects, which is complementary and abrasive in equal measure. It is not a verdict either way.
Why does Capricorn seem cold to Cancer?
Because Capricorn withdraws into work under stress. The withdrawal is a coping method rather than a rejection, and it lands as a rejection regardless.
Do the Moon and Saturn rulerships matter?
They set two very different tempos, one measured in days and one in years. Their placements in the two charts matter considerably more than the Suns.
What is worth reading instead?
The Moon, Venus and Mars in both charts, and the aspects between them. Those describe two people rather than two twelfths of a population.