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

(transportation in Hong Kong) The Peak Tram

always want to be the first to act

to have no connection whatsoever [colloquial]

to stay in a hotel room [colloquial]