Kendo and Demaestro are definitely right - to operate on that scale you're going to need custom code.
You could integrate custom code into a CMS and if you do it as a separate module/plugin/add-on, you'll still be able to run updates without issue, but I don't think you can get there with a CMS and a custom module. There might be some off-the-shelf software made for running dating sites, but I guess none of us here know it. As far as I know, it's all proprietary.
I'm not trying to be a naysayer. As I say, I almost always find myself in the position of telling people not to think about scale. Most people worry about scale before they even have their first customer. But if you're making a dating site and you hope to run at a profit, I think you need to grapple with scale from the outset, otherwise you just create a model for losing more money faster.
use 2 sites
2 sites? You mean two sites or putting your static resources on a separate domain? Like example.com and static.example.com for static resources? You could just use a CDN. But that isn't the real problem. With Amazon Web Services or Cloudflare, that's all easy enough.
Then 10,000 hits will remain 10,000 hits
That's the problem. And that's where Metcalfe's Law comes in with respect to dating sites in a way that it just doesn't with respect to Wikipedia or most content sites.
I assumed he meant 10 million members, not hits. And 10,000 searches on a dating site with 10,000 members is not the same as 10,000 searches on a dating site with 10,000,000 members. And as per Metcalfe's Law, it's not merely 1,000 times harder. It's much worse than that.
So the problem isn't handling the static resources, it's the massive number of possible connections for your dating algo to handle. If you have 10,000,000 members in your database and you need to come up with joins that find
age: 25 < age < 35
hobbies: at least two that overlap
religion: lapsed Catholic
marital status: single or divorced
subscription status: active
And you have to run those queries on 10,000,000 people for 10,000,000 people, you have to know a thing or two about databases, data structures. profiling, etc etc.
Markus from Plenty of Fish (https://www.webmasterworld.com/profile/markus007/) used to be an active member here and had some illuminating posts on what it takes to run a dating site without going broke and why it has particular scalability problems that most sites don't have (LinkedIn would be an exception, but remember LinkedIn was started by a team whose background was... dating sites).
As Markus said "At the end of the day, its all about algorithms and AI and not about platforms/languages." [webmasterworld.com