This is a knot, to be sure. From what little research I have done in the past, there seem to be several accepted views about why they are so different. The most commonly accepted seems to be that one genealogy is from the father's side (Joseph)and one from the mother's (Mary). The Luke passage is generally considered to be Mary's descent and I think this comes from where it says:

And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli,

In verse 23. The phrase "as we supposed" is taken to mean that people thought that Jesus as the son of Joseph, but he was not. Thus, the rest of the line would be Mary's

While this may be commonly held (if I remember correctly) it seems to be a real stretch to me .



This is not really a problem when you consider both the era in which this was recorded, ancient mindsets and all of that. It was very common to list only significant names in a genealogy and to skip names of less significance and who was considered significant would be up to the one compiling the list. Words that are translated "begat" and "son of" and all of that generally are used to show relation and not to be taken literally. So someone may be recorded as the "son of" a particular person and actually be the grandson or great-great grandson.

I am not saying these are acceptable excuses, but this is what little I remember and I really don't want to do the research. I have better things to do .