Yes, you are correct.
God said not to eat the fruit of knowledge of good and evil in Eden and if they ate, they will surely die. But Adam and Eve ate when they knew not it was good or evil, which means they disobeyed while innocent. Now, mankind is facing death for something he did when he was innocent. Man is totally helpless as he is going to die. Throughout scriptures, we have seen God saving and defending the innocent. Now, God wants to save the fallen mankind, but God cannot take His Word back which He said to them, the punishment for eating that fruit. No one can save mankind except God Himself, but not against His own Word who is again God Himself. This made God love man so much because he is helpless and facing death for something he did when he was innocent. So, the Word, who is God Himself became flesh, became a normal man and entered death itself to be victorious over death. So, God saved man through one Man Jesus Christ.
It's not a requirement for God to save mankind but God loved mankind so much because he is helpless and facing death for his innocent act. Since, God loved us, we are supposed to love the same way.
(1John 4:10) In this is love, not that we loved God, but that He loved us and sent His Son [to be] the propitiation for our sins. Beloved, if God so loved us, we also ought to love one another.
Do you love God the same way you love your pizza? In fact loving pizza is not even love. It's a language problem because English isn't that rich
(compared to some classical languages) and it's all called love but I speak another classical language which has the word love defined very accurately based on who we love.
- Love between parents and children/close relatives - பாசம் (paasam)
- Love between lovers - காதல் (kaadal)
- Love between husband and wife - நேசம் (naesam)
- Love towards strangers/general love - அன்பு (anbu)
- Love towards objects/events - ஆசை (aasai)
If you do a translation back to English, all can be translated as love
(yet some affection or desire depending on context). You can use the same 'love' for everything listed above in English but in the other language, you can't use 'kadal' (meant for lovers), for parents and children or strangers or objects/events. You can use 'anbu' for everything except for objects.
I believe such differences exist in ancient Greek and Hebrew as well (not for love specifically but for other words, where meaning and context which that particular word brings out is completely missed out in English and other translated languages).
You can clearly see the different levels of love expressed as different words in a language.