At the moment, all users of Steam own the Dota 2 Spectator client. Due to a configuration conflict, this makes the Steam Store think that you already own Dota 2.
This issue is known and we are currently working on a fix.
Until this fix is implemented, if you wish to purchase an invite for yourself, you can do so here:http://store.steampowered.com/app/570/
Add the game to your cart and select "Purchase as a gift," and then "Store the gift in my inventory to send later" when checking out.
Once the purchase is complete, you can activate the game on your own account with the following process:
-Go to the 'Community' tab in the Steam client.
-Click the 'View Inventory' tab under the right hand column titled 'Actions'. You should now see your current inventory.
-Select the Steam tab. This will open the games/gifts that are currently in your Steam inventory.
-Select the game that you would like to redeem onto your account. There should now be a button which says "Add to my game library" under the description.
-Click 'Unpack Gift' to add the game to your Steam account. Once added the game cannot be removed from your account.
If you have received early access to Dota 2 via Trade or a gift, you can activate it using the previous Inventory step.