@Lisa75 you are right, I just checked, on the mobile version, there is no "pet" to select, just adults, children, and infants.
Please contact Airbnb CS through Twitter or Facebook and complain about it, it is a glitch bc on the desktop you can select the number of pets you travel with and if the listing is "pet friendly" it is written in their house rules, down on the bottom of the page, near the footer.
The irony is when Airbnb sets its website in a way to make guests book as quickly as possible... but the result of its setting is totally opposite, an incredible waste of guests' and hosts' time.
@Quincy @Nick