> Why should my ideas then be anything different?
It's not a "should" -- ideas simply are fundamentally different from physical materials, and the norms we use to deal with the inherent qualities of one don't automatically translate over to the other without a suitable rationale.
Physical materials qualify as property because they are economically rival: one party possessing and using them inherently excludes others, meaning that competing claims to the same thing must be resolved by one party surrendering their claims to the other. There's no agree-to-disagree mechanism available, so we need a way to resolve disputes in favor of one party or another.
There is no clear application of this to non-rival intangibles: there is no conflict between two people using similar ideas independently of each other in the first place. Someone copying your idea isn't analogous to them picking fruit off of your tree, it's analogous to them learning from what you're doing, and then going off and planting their own tree on their own land.
Modern "intellectual property" is a contrivance by people desiring to artificially incentivize certain categories of activity by attempting to replicate one of the downstream effects of the inherent exclusivity of goods, namely commercial markets. So you wind up with a positive-law intervention to create artificial scarcity in order to produce similar second-order consequences to what comes about when scarcity exists naturally.
That's why property rights have been recognized in all civilizations in human history -- and are likely a prerequisite for organized civilization to exist in the first place -- whereas copyright laws in their modern form date to the 18th century.
In fact, artificial "intellectual property" conflicts with natural property rights, in that in claiming a universal monopoly on arranging any bits of matter into particular patterns, you are actually claiming the right to stop people from using their own actual property as they please.