We've been doong FB for almost a year now and have learned alot in this space, (with still alot to go).
Here are some things that might help you.
1. The type of ad you run and the copy you use has a big impact on the user's behaviour. Not all ads are created equal. Good copy that really taps i to why someone should be clicking through and what value they can expect to attain the other end makes a big difference. But this isnt an exact science. Its more of an art.
2. If you're targeting is off, you will also get undesired behaviour. People might click through because they like the ad, but if they havent been targeted correctly, it will cause issues. You may need to get more laser focused in terms of targeting. Age range, custom audience (through email upload), lookalike audiences, interests etc.
3. People via email, trust you to some extent and have a relationship with you. They're a warm audience. This is the real reason the organic approach is working for you. You have a relationship with those people. Its not the same with paid ads. You need to build that trust and warm them up. You might take a layered/re-targeting approach by offering them some value and then re-targeting the people that interact with your content with a second and third round of ads. You might also grab their email and then target them both via email and fb.
FB can work, but it take alot of iterations and time to get it right.
Alternatively you could just run an FB ad that does something to collect email addresses, then run an email nurturing campaign, warm up the audience and then target via email.
FB can work, but it takes time.