To spare one's feelings = It means not saying/doing anything that could make somebody feel bad about themselves. Therefore your sentence "We do not spare the feelings of the learner when it comes to writing mistakes."means the exact opposite.

This means that if a person makes a mistake, "we" will tell them clearly and directly that they have done so. To spare someone's feelings, you would choose your words so that you do not offend that person or make them feel bad about what they have done. These people will not act in this way. So, even if it makes you feel bad, they will tell you (the learner) what you have done wrong.