Because we usually see the Pharisees opposing Jesus, we might overlook that the question of the "greatest commandment" was a real one for first-century Jews. There was no agreed-on answer.
Some religious teachers and authorities argued that the first commandment in the ten -- "You shall have no other gods before me" -- was the greatest. It was, after all, the first one. Israel's failure to limit themselves to the worship of God and God alone opened them to near destruction at the hands of other nations. The proponents had a pretty good case.
Others might suggest the words from the prophet Micah -- "Do justice, love mercy and walk humbly with God." It definitely covered most of the range of human activity and it was a command even if it was not in the Torah or books of teaching itself.
The answer Jesus gave when he quoted Deuteronomy 6:5 was shared by a lot of people as well. It sort of covered the territory of the first one mentioned and it also included direction about actions, such as loving God with all our minds and all our strength. Some of the Pharisees may have really wanted to know what Jesus thought. Remember, not all of them oppose him and some are interested in what he says. They may have been part of the group, even if their leadership is looking for ammo to use in their arguments with the rabbi from Nazareth.
Those people would probably have been disappointed with Jesus' pretty straightforward answer. He gave an answer shared by many religious teachers that had some solid reasoning behind it. Probably every Jewish person knew that verse, called "The Shema" after its first words in Hebrew: "Shema Yisrael!"
But then he gets weird.
The questioners asked for the greatest commandment, and they had to have been surprised when Jesus gave them not just the top commandment but the runner-up as well. "The second commandment? Who asked him for the second one? I don't get this." And their confusion wasn't helped by the content of the second commandment Jesus chose. It's a quote from Leviticus and there's no natural connection between them in the Torah. They're not next to each other and they're not in the same contexts. Both are commands to love, but to first-century Jews the pairing makes as much sense as putting the Shema with the pre-Porta Potty sanitation instructions given in Deuteronomy 23:12-13 or the command to not strip all the grapes from the vineyard in Leviticus 19:10. We see the connection because Jesus drew it, but why did he draw it at all?
If I'm right, a major reason for that connection is to pave the path for sharing the gospel.
We live inside the gospel, so to speak. We know what it means for us to love God with all our heart, soul, mind and strength because we know who we mean when we say God and we know (more or less) what God wants: To be the center and foundation of our lives. But someone living outside the gospel may not know what we mean when we say we will love God that way. They may not know who God is and they may have a wrong idea about what God wants. Someone who meets people who claim to be Christian but only talk about who God hates probably aren't impressed with our determination to love God even though we aren't like those other people. We have to show them what we mean when we talk about loving God -- who God is and how we show love.
We do that by loving our neighbors as we love ourselves. We do that when we try to make sure that, in every case where we can, we find the most loving thing to do and do it. Sometimes we will show compassion, sometimes we will offer help and sometimes we will confront evil, but every time we'll do whatever it is in ways that show love. People who see that may then say, "Well, those Christians show love to other people, so I might be interested in hearing about the God they say tells them to do that."
If anything, time has made the connection more important today! Our culture tends to over-emphasize the "feeling" part of love so much we've made it even easier to say "I love God" but mean next to nothing by it. Popular entertainment leaves out the part where love requires work and action to be real, but if we want to show the world our love for God is real, we have to demonstrate that with actions towards our neighbors. We need to have more than a warm mushy feeling towards a homeless person to help them not to freeze to death. We have to have more than butterflies in our stomach towards foster kids if we want them to have the chance to succeed that their circumstances may deny them. You get the idea.
And if that's how we live, to show real love for our neighbors whom we have seen, to borrow a phrase from one of John's letters, we will demonstrate to them and to ourselves our love for God whom we have not seen.