Try as you might, you're using an Android by Google device, with a Gmail by Google email address, on a device you've agreed to the Google terms and conditions of service to use. I get it, try to volunteer as little as possible but at the end of the day B. Diddy is right, and I think everyone knows or assumes that anything we do on or with Google's device, oops I mean, with our device is being documented, tracked, and used to serve someone ads directly or indirectly.
Check whatever app you're using for Contacts and see if that app has a back-up option. That would be your best bet since so many of them come with backups. If you're using Google Contacts to view, edit or connect to your contact, they already have what they need from you. You're just not getting the free back-up benefit they're offering in exchange for the data they are already taking from you.
In the end it's up to you however you decide go, it just seems like more hassle when all of your stuff can be anywhere you can connect to the internet verses, something like MyBackUp Pro. Oh, it will back up everything and save it to a cloud service of your choice but if you're at work on your computer you can't just log into MBUP.
Good luck.