There a mechanisms by which additional indexes could cause a slowdown:
Most optimization decisions are designed for the worst case – when you're accessing data that is too large to fit into any cache and has to be loaded from disk.
If the data itself fits into the caches, but all the various indexes used by your queries are so large that the entire working set becomes too large, you will get more swapping.
SELECT queries will ignore any indexes that are not actually used. However, INSERT/UPDATE/DELETE statements must update all indexes of the changed table, so every additional index will slow down such changes.
Use EXPLAIN QUERY PLAN to check which indexes are actually used by a query.
Read Query Planning and The SQLite Query Planner to understand how indexes can be used.