I can reproduce this, I think it's actually a bug in facebook's captcha mechanism.
From what I can see, it's requesting
/tfbimage.php?captcha_challenge_code=foo&captcha_challenge_auth=bar and that request is itself receiving a redirect to
/login.php?next=<the previous URL for the captcha image> which obviously doesn't return a captcha image.
Essentially it's asking you to login to retrieve the captcha (which you're probably getting...because you're not logged in. derp.)
Google's recaptcha did a similar thing previously on cloudflare, where requests for the captcha image got 403'd (Forbidden) so you couldn't fetch the mechanism to show you weren't a bot...because it thought you were a bot.
In my case a workaround is to click the
Try another text button which then seems to produce a usable captcha.
There's not much else to be done from your side except try the workaround, it looks like an issue (or an intentional tactic? ¯\_(ツ)_/¯) on facebook's side