Well, there are two sides to that argument. Why we should not date multiple partners, and why not we date several people at once.
While girls go for the first argument, guys definitely jump on the second. Dating is not harmful per se, but there are various issues one can face while multitasking with dating.
Lets begin with the 'against' side first. During a person's trails to get to know several people at once, there could be mixing up of facts and information. It is obviously risky to give one person's birthday gift to another person. Imagine the drama! Also, those who date more than once person at the same time are attention seekers who are not looking for a long term relationship. It could be heart breaking for the partner who is at the receiving end.
More importantly, the comparisons that inevitably crop up spoil the experience for all individuals in the triangle. Or is it rectangle? Every person seems to lack in something or the other. Besides, it sets the ground for a dumping session.
Coming to the 'for' side, dating more than one person widens up your horizons. It helps you analyze who or what makes you more comfortable. It gives the person more options to choose from while looking for a partner. This happens more so in an arranged marriage setting. Nevermind that the parents are as involved in the 'dating' as the children.
Dating with multiple people allows you to make quick decisions over whether you want to take it forward with the person or not. However, it is necessary to set the expectations beforehand. At the end of the day, for or against, dating comes with its own tricks and treats.