The security of your online accounts is critically important. That's why Instagram and Facebook have an official program to review and approve applications.
Approved apps require you to login with Instagram/Facebook, which is why we have that requirement as well. The benefits of this are:
You don't have to directly share any personal information
There are restrictions on what data we have and how it can be used
You can revoke the integration and request to have your data deleted at any time
Your account can only be used in approved ways
You don't risk getting your account banned for inappropriate behavior
What to be careful of
You might see other apps (especially giveaway apps) that do not require Instagram/Facebook login. While this might seem attractive, they do this by using unauthorized methods like scraping instead of using the official authorized Instagram and Facebook APIs.
When they do this on your behalf your account is also using these same unauthorized methods, which jeopardizes your account. That's why Instagram and Facebook clearly state to avoid doing this in their Terms of Service.
Logging in with Instagram/Facebook may seem like a hassle, but POPSMASH, Instagram and Facebook require this for the safety of your account.