Why does steam keep asking if I'm over 18?
It's definitely by design. From this topic:
Tito Shivan (Steam moderator):
As mentioned, the client does save the age. And whether it's saved or not, they won't disable the step of having to click and accept before entering the game page. It's a feature to remove any responsibility from Valve in case anyone not meant to visits the page (hence lying about their age)
It's a way to avoid stupid lawsuits.
The thread also mentions law texts excerpts that may help to understand. For example:
2.2 If the audio-visual content contains material from a Mature-rated or Adults Only-rated game (or one that is anticipated to receive either rating), display an ESRB-compliant age-gate prior to access or purchase.
You can now skip that validation step entirely:
The age verification date is stored locally only. You can see this for yourself if you login to Steam with your browser in Incognito mode, or after having cleared your cookies. It is never stored on Steam's servers at all, likely due to potential privacy concerns (or they just didn't feel like storing all that data).
There's no real way to bypass the age-gate either. The ESRB's guidelines are rather specific about an age-gate system that cannot be circumvented or gamed (if you tell Steam that you're 14, it will store a session cookie that won't let you go back and try again). The best you can really do is just deal with it, and be thankful that at least Steam is smart about keeping your birthdate (or fake birthdate) stored somewhere.
The question of "why" has been already answered, but for the "And how can I make it stop doing that" part while it's not possible in the client itself, Enhanced Steam browser plugin offers an option to skip the age gates if you want to (among other features). It's available for Chrome, Opera and Firefox browsers and there's a separate stand-alone client too.