Why is CI much wider than 1.96*sem for very small samples?

For large samples the relation between confidence level and critical value is unambiguous as indicated in the table below: 95% CI = mean +/- 1.96 * sem 98% CI = mean +/- 2.33 * sem

For small samples the relation between the 95% CI and the sem is not determined by the critical value 1.96 but the critical value depends on the sample size.

For very small samples (n=2 or 3) the critical value is much higher than 1.96 In this case, it might be better to just show the data without error bars.