Now, before you start thinking that I'm of the belief that man is inherently bad, let me explain. The scriptures teach us in multiple places that we live in a fallen world, and are thus fallen beings. The joyous goal of this life is to learn and grow, with the guidance of the Holy Spirit, so that we can return to our Father in Heaven in a not-so-fallen state. His preference, really His Plan, is that we return in a perfect state. But, while we are here, that's not the case. We are fallen. We are imperfect, simply by nature. And many of the sacrifices that were made anciently were to acknowledge that. As well, of course, as to symbolize that the real way to overcome our imperfections is through the Atonement of Jesus Christ. Offerings for trespasses against God also have this purpose; however, if I've read correctly, these offerings are more specific as they are done when certain sinful acts are committed.
Thinking about the difference between these two types of offerings gives me perspective on what kinds of sacrifices we offer in our lives. We don't only need to sacrifice for the Lord when we do wrong things. That is crucial and part of repentance, but we also need to sacrifice simply because we are fallen and require His Atonement in order to work towards being whole. Every day. This doesn't mean that we are terrible and without sacrifice we "totally suck." It means that with sacrifice, which is essentially acknowledging that our Father in Heaven owns all we have and Christ is responsible for our ability to repent and progress, we gain more perspective into how the Lord can help us. As a result, we become (if I may say so), not-so-fallen. Or at least, a little less fallen every time we sacrifice our time, talents, resources, or anything else to Him.
Another thing I've been pondering on is how Jesus Christ is all parts of these symbolic ancient sacrifices. He is the Offering, the Offerer, and the Priest. I had always thought of us as the Offerer, so this helped me see sacrificing for the Lord in a less selfish way.
Think about it.