Why does chemisorption decrease with increasing temperatures?
Let's answer this question with the help of some thermodynamics and kinetics. Chemisorption is a chemical process with $\Delta S&lt;0$ and $\Delta H&lt;0$. Thus, in simpler words it is an enthalpy driven exothermic equilibrium
Every chemical process is an equilibrium with varying extent of completion. So your idea of chemisorption not being an equilibrium is wrong. Every chemical reaction is theoretically reversible in nature. What we call irreversible reactions in general are such reactions which are heavily favoured on one side of the equilibrium.
Now,
$\ln K = -\frac{\Delta H}{RT}  + \frac{\Delta S}{R}$
It is evident from this above expression that the $K$ will decrease when we increase $T$ when $\Delta H&lt;0$ and thus the aforementioned conclusion.
But this is only half the story. Like all other chemical reactions, chemisorption also needs some activation energy to overcome the transition state. At lower temperatures there are very few molecules which have the kinetic energy enough to overcome the activation energy. The fraction of these molecules increases with increase in temperature and thus increasing the extent of chemisorption.
Conclusion
Due to the combination of thermodynamic and kinetic effects the rate of chemisorption first increases with the increase in temperature but after a certain saturation point the thermodynamic effects start dominating and thus the extent of chemisorption starts to decrease.
The graph below might help you understand how the extent of chemisorption changes with change in temperature.

Here,
$x$ = Mass of adsorbate
$m$ = Mass of adsorbent