This is a very common problem across the entire RTS genre, but I find that from one player to the next there's often very different reasons for doing this.  Without hearing your friend's particular vantage point, it's hard for me to gauge what specifically his issue is.  Certainly having been penned in repeatedly, he must understand the urgency of expansion, but still isn't doing it.

If you're just looking for words to put it succinctly, I recommend "time is money".  If your opponent is "spending" his time and you are not, he's going to reap the advantage of having done so.  Being idle, even for a short period of time, is equivalent to throwing away some of your resources.

Not just RTS games, every strategy game that has a resource system rewards turn advantage. Explain it to your friend this way: The extra income you get from expanding more quickly can be reinvested into more ships, more technology and more structures which increase your aggregate advantage over your opponent. The sooner you obtain and use these advantages, the sooner you'll be able to obtain yet more turn advantage.

Expansion is doubly important in Sins, because there's a finite number of planets which can be held. Simply put, every system that you cede to your opponent essentially costs double. First is the lost income you don't have the use of, and second is the extra income your opponent will have, which, if he's remotely competent, he will use to come crush you, taking away more territory, and extending his advantage.

I don't know your friend so I don't know where he's coming from but...

Sins was actually the first true RTS game I played...my closest experience to RTS before sins was with total war games...everything else was turn based (SMAC/X, Civ, Gal Civ II, etc...)...

The biggest issue for me was being overly cautious...in many turn-based games, vertical expansion is a viable alternative to horizontal expansion, and both strategies are rewarded and can win...however, in sins horizontal expansion is far more dominant...

If you can get your friend to actually expand quickly just once, it will give him confidence in horizontal expansion and he'll have no problem doing it again...it's breaking that initial barrier and getting him to do it right the first time...

Having a fixed procedure that is tried and true can help...it isn't good to always stick to the same rules, but it's still a good place to start learning...one way of doing this is for you two to play on the same team against an AI...as you do things, tell him to do exactly what you are doing...if you build an akkan, he builds a colony cap...if you attack your nearest asteroid with 4 LFs, he needs to do the same...it may be annoying and inflexible but a step by step approach may be the only way of removing his doubts and convincing him that rapid expansion not only wins, but is much less risky than it seems...