Why can't countries be awarded 9 or 11 points at the Eurovision Song Contest?

The point system is explained here.

https://en.wikipedia.org/wiki/Voting_at_the_Eurovision_Song_Contest

As for this specific question, from 2009 to 2015 the points worked like this:

"All countries used televoting and/or SMS-voting (50%) and five-member juries (50%), apart from San Marino which was 100% jury due to country size. This is so called jury-televote 50/50. In the event of a televoting failure, only a jury is used by that country; in the event of a jury failure, only televoting is used by that country. The two parts of the vote were combined by awarding 12, 10, 8-1 points to the top ten in each discipline, then combining the scores. Where two songs were tied, the televote score took precedence."

So the answer to this question is "because that's the way they made the system".

It sort of makes sense.... you can give 12 points to set your #1 choice apart, then 10 points for your second choice, and then 1-8 points for the rest.

It lets you give more weight to your #1 and #2 choices.