There could be a few reasons in which you are unable to create an account/log in and these are listed below.
You need a Microsoft Account
A Microsoft/Xbox account is required to log into the forum as this gives info for your account (i.e. email, gamertag, profile pic, etc.). You can easily sign up for a Microsoft account when you click “Sign Up” at the top of the forum.
Clear your Cache/Cookies
There could be something held in the cache that could be preventing this. While how you can do this varies from browser to browser, a simple search can answer your question on how to do this
You already have an account
You can always try clicking “Log In” at the top and see if you already have an account.
The forum was/is down for maintenance
Sometimes the forum is down when you try to create an account. If this is the case, try creating/logging in an hour to two later.
Your browser isn’t supported
Try using another browser 
You have been suspended/banned from the forum
Typically if you are banned/suspended and you try to log in you will get an error message stating you have been. If you want to appeal a ban please refer here: https://flightsimulator.zendesk.com/hc/en-us/requests/new
Your browser needs an update
Typically this is shown at the top right corner of your browser app. As always, a quick web search will answer your question about how to check your browser for an update.
I forgot my email/password
Once again, as the backbone of your forum account is your Microsoft account, follow the steps on the Microsoft Log in page if you forget your email or password.
I am still having issues
If you are still having issues please create a ticket here: https://flightsimulator.zendesk.com/hc/en-us/requests/new and you will be assisted.
If you have a workaround that works for you but is not listed on here please message @HamMan2118 (me!) and I’ll add it.