Notice the phrase "being built up." It is active and dynamic, indicating that the building is being done by somebody else.
Peter calls us living stones. Step away from the idea of human beings and imagine stones out in a field or a pile of bricks. Peter's illustration is of a construction job. In his mind's eye, as he was writing this, he saw a literal building being built by a stone mason, God, with His Son Jesus Christ.
We are "being built up." The stones are not taking themselves out of the field, shaping themselves, and fitting themselves into the building. Somebody else is picking up the stones, knocking off the rough edges, and fitting them exactly into the place where the Builder wants them to go. Peter is describing a building that is not being constructed haphazardly but according to an intelligent plan, as if the Builder is working according to a blueprint drawn far in advance of construction.
"Chief cornerstone" is mentioned in verse 6, and like the chief cornerstone, each of us, as living stones, are being individually set apart from all of the other rocks in the field, then prepared and fitted into what is called "a spiritual house." The word "house" simply means a dwelling place, and since this is a spiritual house, it implies "a dwelling place for God." The picture Peter wants us to imagine is that each one of these stones is chosen individually and pulled out of the field, fitted and shaped, and put into the building.
We see sanctification at work in this. In Peter's illustration, the stone mason looks over a selection of stones in a field, but only chooses certain ones, which he then crafts to His specifications for its place in the building. It shows Christians being transformed into a suitable dwelling place for God—individually and as an institution, as a church. This begins to place responsibilities on each of the living stones that are set apart and made a part of the dwelling place for God.