Quantitative experimental methodology is about discovering the differences that result when ONE factor is changed. Therefore, you have a control group and an experimental group. In the experimental group, the factor is changed from "normal" and in the control group it is not. This allows you to identify the differences that result.
But qualitative methodology is NOT about studying differences. It is about studying experiences and perceptions of your participants. In most cases, it is not informative to interview people who have NOT had the experience, so it is not relevant to have a control group.
Thats why some qualitative researchers have utilized sequential case studies to develop and test theory in a manner similar to experimental method, but in this case its considered comparison rather than control measures.
If you compare two cases where an important element is present in one but that not in the another, this is similar to "control," but you would still need to do careful qualitative research to determine the influence (if any) of this difference.
Case study research: design and methods by Robert K. Yin is a very good source on comparative case studies.
Mohanad Kamaleldin Mahmoud Ibrahim -Thank you for your question. In quantitative studies, the aim may be to study the effect of an intervention (for example, a drug, a chemical, or a teaching method). We always need to have a control group to compare the two groups and examine if the effect is due to the intervention, or there is no difference between the two groups. The design should ensure that there are no differences between the two groups other than the intervention caused in the experimental group. Therefore, we need a control group for two reasons- to prove that the intervention causes the effect, and to measure the p-value (calculate the significance of the difference).
Only quantitative research will use statistical tools to unequivocally prove validity. If, as a qualitative researcher, you feel that the gender of respondents may be a factor, you are free to choose to interview e.g., only female respondents. Then you have controlled for gender! It is no longer a factor!