Might they found something more interesting

ask for permission? u should break up, have some honor and dignity!

she want to try him in bed.

Really? Quite the tit for tat statement, which is incorrect:

They feel underappreciated, neglected, or ignored.
They feel more like a housekeeper, nanny, or financial provider than a wife or girlfriend. So they seek an external situation that validates them for who they are, rather than the services they perform.

They crave intimacy. Women tend to feel valued and connected to a significant other more through non-sexual, emotional interplay (talking, having fun together, being thoughtful, building a home and social life together, etc.) than sexual activity. When they’re not feeling that type of connection from their primary partner, they may seek it elsewhere.

They are overwhelmed by the needs of others.
Recent research about women who cheat indicates that many women, despite stating that they deeply love their spouse, their home, their work, and their lives, cheat anyway. These women often describe feeling so under-supported and overwhelmed by having to be all things to all people at all times that they seek extramarital sex as a form of life-fulfillment.

They are lonely. Women can experience loneliness in a relationship for any number of reasons. Maybe their spouse works long hours or travels for business on a regular basis, or maybe their spouse is emotionally unavailable. Whatever the cause, they feel lonely, and they seek connection through infidelity to fill the void.
They expect too much from a primary relationship. Some women have unreasonable expectations about what their primary partner and relationship should provide. They expect their significant other to meet their every need 24/7, 365 days a year, and when that doesn’t happen, they seek attention elsewhere.

They are responding to or re-enacting early-life trauma and abuse. Sometimes women who experienced profound early-life (or adult) trauma, especially sexual trauma, will re-enact that trauma as a way of trying to master or control it.

They’re not having enough satisfying sex at home.
There is a societal misconception that only men enjoy sex. But plenty of women also enjoy sex, and if they’re not getting it at home, or it’s not enjoyable to them, for whatever reason, they may well seek it elsewhere.

The reasons men use to cheat are entirely different, like immaturity, selfishness,
insecurity, etc. etc. you can read them here. http://www.psychologytoday.com/us/blog/love-and-sex-in-the-digital-age/201704/13-reasons-why-men-cheat


I can add another reason for cheating, not by women, by men: out of spite, to hurt his woman.

Nice women ask for permission.

Of course they do

Oh honey, is it okay if I cheat on you? Will you give me your permission?

It isn't cheating if you have permission. Can you leave one of your girlfriends who may be complaining she is not getting enough with me, while you have a girls night out with the rest of your girlfriends.