Les pronoms demonstratifs

You're right: because of the female version of stricte, it should be celle-là.

Since professeur is masculine, even when referring to a woman, I would have expected celui-là est strict. I wonder why you assume that there is a feminine adjective at the end?

Agree with Alan - ‘celui’ refers to the noun ‘professeur’,  and it is the noun gender that is grammatically determinant. If you have seen this in a lesson here, you should report it for correction. 

If you used ‘deux personnes’, it would be celle-ci and celle-la and adjectives agreeing in the feminine. 

On the other hand, with the 2 people clearly identifiable to the listener, you can easily distinguish between them with,  ‘Il est…’ and ‘Elle est..’ or names, rather than by ‘place/position’.

Thank you Chris, Alan and Maarten.  

This was a question I found in one of the exercises related to pronoms demonstratifs.  

Parmi les deux professurs _______ est aimable mais, _________ est stricte.   

The adjective "stricte" was already in the given sentence.  Thats how I arrived at celle-la which could be more suitable as stricte was feminine. 

Further explanations would be appreciated. 

Thanks Jaya. If this ‘mixed use’ is correct, I have not come across it before. I guess it could arise from accepting that ‘professeur(e)’ in the singular could be either masculine or feminine - le professeur or la professeur. None of the lesson examples cover this as far as I can see, so it would be useful to have an example and brief explanation. 

Yes, I would expect that people align the use of celle-là and stricte to the natural gender of the person they refer to when it is obvious. Otherwise, it would sound quite rude to my ears.