Google Translate rates hard as the second most popular usage of fort. Reference.com places it sixth. Larousse puts it in fourth place.
If Duo doesn't want to consider hard for fort then they shouldn't put it into a list of options on a multiple choice question for fort.
In such a short phrase I wouldn't expect hard to be a reasonable usage but it is possible in some contexts. Obviously a fair number of contexts actually.
Yes - thanks for your reply but my question was why then is it 'I am strong' and not 'I have strength'? If 'I am strong' is correct then why not 'I am cold'?
language is arbitrary - the question you pose is already assuming that it is better to have it only one way for everything. Having arbitrary rules, having different things working differently is interesting.
For english something similar would be: Why does bough sound like bow and rough sound like ruff when it's written the same "ough"?
http://www.frenchtoday.com/blog/chaud-and-froid-in-french that's why. "J'ai " used when talk about cold or heat
"Je suis fort" but "j'ai claud". I know that I shouldn't try to understand it by English grammer. French must has its own rules. However I just want to know in what situations should I use"être" and when "avoir"? like if there were two groups of words which follows "être" and "avoir" accordingly?
One reason is that this site doesn't know whether a user is male or female, therefore it uses its default setting, which is the masculine form. Yes, I now know what you're thinking; you're thinking that that's sexist and while that can be considered so, it's good to get used to using the other form.
The other reason is that "fort" sounds like "four" and "forte" is pronounced like the masculine form "fort".
Just because you're female, doesn't mean you have to use the feminine form. The site tells you which gender to use. Just remember that and you should get everything right that concerns gender.
You can use the feminine form when you're not using Duolingo.
Hope you understand.