They are just having a shitting match over who arrives first.
shitting match
idiomA pointless competition, dispute or conflict, often over some trivial matter.
Origin
disputed originCompare pissing contest.
The meeting turned into a total shitting match over the color of the office walls.
The two managers engaged in a pointless shitting match, completely ignoring the urgent project deadlines looming over their department.
- 01
be no match for
To be outmatched by; to be much weaker, less capable, or less desirable than.
- 02
game, set, match
An expression indicating finality, announcing that a series of events—usually involving some form of rivalry—has reached a conclusion.
- 03
match made in heaven
A relationship, such as a marriage, that is happy and successful, sometimes because the partners are very compatible.
- 04
match made in hell
A relationship that is likely to be unhappy or unsuccessful because the two partners are very incompatible with each other.
- 05
whole shooting match
Everything; the entire collection, endeavor, or activity.