Likert scale is very popular in customer/client/consumer/patient/student/.. satisfaction survey (CSAT) but care and clear assumptions of use are often a concern (including mine The Sin of Taking the Measure To Be the Goal. https://www.gotoknow.org/posts/713359 ).

In short: Likert scale assigns responses to categories (set members) denoted by ‘numbers’. These numbers are ‘arbitrary’ and not ‘metric’ (for use to measure). This means (as you stressed a number of times) 3 is 2 times more than 1 (but because ‘we rank’ 1<2<..<5), we can only say 3 is better (in the eye of the surveyor) than 2, than 1. In many cases/surveys, questions are design to cover target areas and expected/forced responses to cover the range [-ve, 0, +ve] symmetrically and equally (in number questions) and ‘assumed’ responses to be samples under Central Limit Theorem, and apply analyses of CLT (normal distribution).

One forgets that standard deviation (sd) or arithmetic has no meaning for sets (categories). Only the counts of responses for each category is useful in ‘Probit’ or ‘Logit’ analysis.

It’s time we look under the hood of statistics and advance our CSAT surveys.