Idiom or expression that would imply "someone is showing equivocal behaviors that indicate a feigned reluctance"

I'm looking for an idiom or expression that mean "someone is showing a feign reluctance to do/ have something" or "someone pretends to be less interested in something or someone than they really are."

For example:

1-Mary claims that he doesn't like issues related to marriage at all, but follows her colleagues' wedding news eagerly.

2- John claims that he doesn't like his classmate,Jane, but it is obvious that he gets jealous of seeing her walking with other boys.

3- Joe asks his GF, Susan, to end their relationship; but calls her again in the evening!(and this is a repeatative story in their relationship, so Susan doesn't know if he really loves her or not, his behaviors are equivocal).

I want to describe such equivocal behaviors that indicate a feign reluctance.

Susan: I'm fed up with Joe's equivocal behaviors, sometimes I get confused and don't know what he is looking for in this relationship, I think he ___."

I have found "to play hard to get" but I'm not sure if it is used for non-romantic relationships (including political ones) or for issues other than relationships too (like my first example).

PS:

In Persian we use this expression:

"Somone pushes it aside with their hand, (but) draws it nearer with their foot." (Here, 'It' refers to the given issue.)

Disingenuous — Cambridge

(of a person or their behaviour) slightly dishonest, or not speaking the complete truth.

"It was disingenuous of her to claim she had no financial interest in the case"

Put on an act — TFD

to pretend that one is something other than what one is.

"Be yourself, Ann. Stop putting on an act." "You don't have to put on an act. We accept you the way you are."

Playing dumb — TFD

To pretend that one has no or little knowledge (of something); to act ignorant or uninformed (about something).

"I don't think I'm supposed to know that Rick is getting fired, so I'm just going to play dumb the next time I see him."

A: "Did Tammy ask you about my date with Steve?"
B: "Yeah, but I played dumb about it. I just couldn't handle more of her drama today."

For #1 and #2, you could say that John and Mary protest too much:

"The lady doth protest too much, methinks" is a quotation from the 1599/1600 play Hamlet by William Shakespeare. It has been used as a figure of speech, in various phrasings, to describe someone's overly frequent and vehement attempts to convince others of some matter of which the opposite is true, thereby making themselves appear defensive and insincere.

(via Wikipedia)

In #3, one might describe Joe as running hot and cold: