In a way, you never really leave once you've been initiated since at that point, you've learned all of their "secrets." Still, it's not uncommon for people to drop after initiation. You hope there will be this amazing bond with your sisters/brothers but it just doesn't always happen for everyone and some people decide it's better to formally drop than keep sinking money into something that doesn't suit them. As much as I hate losing money on that badge, it's still less than 1 month of dues.
Things like networking are the selling point but in reality, it's all about partying and social stuff. Especially for the groups considered social organizations. The service fraternities and sororities (academic, music, engineering, etc.) are more serious and focused on their service background, but even they have become more about partying over the years. The social ones, like mine and Kendall's, have academic and philanthropic angles, but most kids enter recruitment because they want access to better parties and the fun/encounters that go with that. It's rarely admitted, but it's the truth.
Sorry...I forget that the terminology isn't part of everyone's common vernacular. It was drilled into my brain over 3 decades ago. What's funny...Greeks all call that glorified pin a badge, but if a fraternity guy decides to show he's serious about a girl he's dating and wants to go a step beyond a lavalier with his letters, he'll "Pin" her. So, she gets a sweetheart version of his formal badge, yet nobody calls it being badged.