I have run into this dilemma on more than one occasion since purchasing my unlocked Nexus 6 for use on Verizon. The person you are talking to asks a question, you know where to find the answer, but you have to go online to get the answer. This was one of the key features when Verizon made the switch to sim cards a few years back. This feature was broken on the unlocked Nexus 6 when being used on the Verizon network. It does appear that Google has fixed this in Android 5.1 with the new VoLTE addon.
To activate this you will first need to log onto your account on the myverizon website and turn on the HD Voice feature which is free. From the dialer type *#*#4636#*#* to enter into the hidden settings menu. From there you will need to choose "Phone Info", then tap the option "turn on volte provisioned flag". When finished reboot your device. Next go to your phones normal settings, tap the more option under wireless and networks, then tap cellular networks, the option for enhanced 4g lte mode should now be turned on. Enjoy surfing while talking without wifi!