Text messaging has always been a lot more convoluted when compared to email messaging as far as universal compatibility. It makes no difference with what email service you use and what email service your recipient uses, exchanging email messages just seamlessly work. But with text messaging, it's a mixed mess of proprietary and open standards that different corporations rely upon as their defaults so as far as all of us, the consumer, we're kind of screwed over. Email messaging was like that in its early days way back but all that nonsense faded away after all the pissing matches settled down. Text messaging doesn't appear to be going that same route however.
Currently, SMS and MMS are the only two standards that all the text messaging apps (Android and iOS) and services (carrier-specific, WhatsApp, iMessage, etc.) support. So while an iMessage to iMessage exchange takes place through Apple's online servers (or the same with WhatsApp to WhatsApp users), when it involves text messaging exchanges between different carriers, that's when things become more problematic. Part of that problem is SMS and MMS are very dated protocols that are are only able to marginally keep up with today's Internet communication needs. SMS also being a very low-bandwidth way of communication, a SMS message can travel over just a basic cellular connection, no mobile data required. MMS does involve a bit more bandwidth so it does require mobile data (or when some carriers allow, over WiFi). Another issue is the file size of MMS attachments are restricted by different carriers using arbitrary limits, so a lot of them will automatically and on-the-fly scale down the resolution of some photo or video files to minimize their file size. (This isn't an issue when it involves iMessage to iMessage as all those exchanges go through Apple servers, no matter which carriers are involved.)
So with MMS, you may or may not have file size issues involved, you may or may not have carrier-exchange issues involved, and you might have a WiFi or mobile data issue involved. Plus, lately Google has been making a very concerted effort into making RCS as the Android equivalent of iMessage with Apple users. But keep in mind that Apple has made it clear it will not support RCS in its iMessage app so SMS/MMS will remain as the only way for Android and iPhone users to exchange messages.
You might want to try using a different text messaging app, if you're using the default app on your Verizon phone a third-party app might negotiate these MMS drawbacks better, and will most likely have a better feature set and allow more user interface options. Or use email instead for attachments (but note with so many security issues tied to things like ransomware and all these days, file attachments are becoming a real issue). Or if you sync your phone with an online storage service like Google Photos, Google Drive, OneDrive, etc. just send a sharable link as a SMS instead of a MMS. Another option is to use a temporary file sharing service like Firefox Send (which despite its name will work in other web browser apps) and send a SMS with the sharable link in it.
