Is it bad to have index space larger than data space?
Think of index design like a sliding switch. You can move this red triangle switch knob anywhere along the line that you want:



I don't usually measure it in terms of size - I usually think of it in terms of index quantity, but size would be fine as well.

It sounds like your DBA thinks the switch is too far over to the right - that you've added too many indexes, and deletes/updates/inserts are performing too slowly. 

Rather than arguing about where the switch is, try asking him about the performance problems you're having due to the high number of indexes. Maybe your users are complaining about delete/update/insert speed, or he's seeing lock waits, or he's having a tough time backing up the database due to its size.

My starting point is usually 5 and 5: around 5 indexes per table, with around 5 or less fields per index. There's nothing magical about that number - it just comes from the fact that I have 5 fingers on each hand, so it's easy to hold my hands up and explain the rule.

You may need to have many LESS indexes than 5 when your workload is heavily biased toward delete/update/insert operations, and you don't have enough hardware horsepower to keep up.

You may be able to have many MORE indexes when your workload is mostly read-only, or when you heavily invest in hardware (like cache the entire database in memory, and have all solid state storage underneath it.)