Why should the paper chromatography strip not touch the walls of the test tube during the analysis of a mixture?

Because the solvent will release to the walls of the test tube and your chromatography will be incorrect.

Explanation:

When you use a paper strip and a solvent in an experiment, you put your sample in the middle of the paper, in that way, the solvent will rise up, separating the different compounds in your mixture, and at the same they are going to be aligned, so will be easier to identify the number of compounds that you have. If you do not put it straight, you will not see clearly the separation, because some compounds will be overlap.