The analogy most often given is that using preliminary tests of normality and equality of variances to decided whether it was safe to use the equal variances assumed version of the t test was like sending out a rowboat to see whether it was safe for the ocean liner. Today, common practice is to avoid preliminary tests. Important violations of the requirements will be detectable to the naked eye without a formal significance test. The worst situation occurs when one sample has a much larger variance and a much smaller sample size than the other. Serious distortion of the P value can occur when the skewness of the two populations is different.
Outliers can distort the mean difference and the t statistic.
They tend to inflate the variance and depress the value and corresponding statistical significance of the t statistic. The separate variances version rarely differs from common variance. When it does, there's usually a problem with the common variances version. When sample sizes are large, the Central Limit Theorem takes over. The two populations of individual observations need not have the same variances.