Don't Mormons believe that Jesus and Satan are brothers?

I find this question very annoying. So I want to explain some of the background beliefs of Mormons. We believe that you and I, and every person that has ever lived since Adam, are children of God. Not in some strange mystical sense, but in the sense of God is the father of our spirits.
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We believe that each of us is composed of a spirit (child of God) and a body (child of our biological parents). The difference, for Mormons, between animals and people, is that animals are creations of God, while people are children of God. So while scientists find more and more similarities between us and other animals, we see the huge differences as a natural result of our different provenance. To me it seems quite easy to understand: those with a mind that can think and a voice that can talk, etc. are children of God. Animals aren't that way.
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We believe that before this earth was made, we all lived with God (whom we often refer to as Heavenly Father). At that time, we were all spirit brothers and sisters. We also believe that angels are children of God. They too are our brothers and sisters. We believe that they are messengers of God, and follow the same path as the rest of us. Quite probably they were/are drawn from the very faithful children of God. Anyway, at some point, as it is written in the Bible, there was war in heaven. We believe a third of the hosts of heaven rebelled, and were cast down. Satan was the leader of the rebels, while Jesus and Michael (who we believe came to the earth as Adam) were the leaders of those that did not rebel.
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We believe that the rebellious third never received physical bodies, while those that followed Jesus did receive bodies, including everyone that has ever lived. In any case, we believe that all of these groups, including people on the earth, spirits that haven't yet been born into the world, those that rebelled against God, angels, etc... pretty much all sentient beings... are children of God. And because they are children of God, they are also brothers and sisters.
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So do we believe that Jesus and Satan are brothers? Yes of course. Not in any special, weird way. Just like you and I are siblings, or you and anyone else. Spirit children of Heavenly Father. When this question of Mormons believing that Jesus and Satan are brothers is brought up, it just seems to me that it's like... "How offensive! How could they believe that? They must be devil worshippers" or something.
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A person may not agree, or may not have beliefs as detailed or as simple as far as who we were before we were born... but a lot of these things are mentioned in the Bible. For example, when the bible refers to Jesus as the "first begotten" like in Hebrews 1:6, we see that as Jesus being the first/oldest spirit child of heavenly father, while references to the "only begotten" like John 1:14, refer to his birth to the Virgin Mary. All the rest of us have a biological father, whereas Jesus was "the" son of God.
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It's one of the things that I really like about the LDS church. We don't have a lot of questions about some of these very basic issues, like Where were we before we were born, Why are we here, What happens when we die, etc. We believe that we have prophets and apostles today that are similar to those of ancient times. They can answer all the burning questions about what we need to do to be saved and also about moral issues of today. The church's website is http://mormon.org/ if you have questions from a more official website.
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I appreciate comments, questions, opinions, and dialogue. Thanks!