a hawser, a thick rope

Literally, a big rope cannot push it together, Metaphor relationship between two people is not close, or did not have any relationship.

two things / people are so not relevant; two things / people have absolutely no relationship

The Peak Tram

noun; tug of war; Contest in which two teams pull at opposite ends of a rope until one drags the other over a central line.

to take the lead

noun; Tug of War Contest in which two teams pull at opposite ends of a rope until one drags the other over a central line.

tracker (spoken)

leading the pack; act or speak first

to make a clean break from a relationship; to sever ties; to cut off the ropes of a steamboat from a ferry; to take drastic measures to halt investment activities in order to minimise the loss of money

stranded cable

always want to be the first to act

to have no connection whatsoever [colloquial]

to stay in a hotel room [colloquial]