Okay, so if I had to guess, I'm going to guess that you don't have much of a credit history. The main way that brokerages do verification is through a variety of databases (including the USPS, Equifax, and the like). If you've moved around frequently, recently changed your phone number, or unknowingly inherited a cell phone number from someone shady, then those databases might be raising red flags.
Your brokerage does not want to go through all this to get your business. It's an added regulatory burden in place to prevent identity theft and money laundering. And yes, you do need to have a phone number on record to get a brokerage account. Brokerages need to have ways of contacting you, including by phone, and getting a phone number also shows due diligence on the part of the brokerage.
Your choices are to send it in, or try a different brokerage. If you do try a different brokerage, and this happens again, contact Equifax and update your contact information there. That should smooth things out in the future.