BGP without default route

I have a scenario below and my question is why do I need the default route site1 and site2 router so that they can ping each other. Without the default route, I can see network via from router site2. But why I cannot ping

net diagram
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From what subnet are you ping'ing?

What do you mean you can "see via"?

To get to a host that is not on the same subnet, each L3 device must know who to route the request through.  Without a default route, you would need a specific route.  Without a specific route or a default route a device has no idea who to route the request through, so it just drops the packet.
You need to have some kind of IGP (static route, OSPF, something) to get between the LAN routers and the Site routers. Even if you are running iBGP between them. And unless you have a number of static routes pointing to the other site, you need a default route on the LAN routers  for the LAN routers to know where to go for external routes.
leblancAccountingAuthor Commented:
"What do you mean you can "see via"?" The sh ip ro from site2 router shows that there is a route to via 10,10,10,1. But I cannot ping

site2 router (without the default gateway):
site2#sh ip ro
Codes: C - connected, S - static, R - RIP, M - mobile, B - BGP
       D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
       N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
       E1 - OSPF external type 1, E2 - OSPF external type 2
       i - IS-IS, su - IS-IS summary, L1 - IS-IS level-1, L2 - IS-IS level-2
       ia - IS-IS inter area, * - candidate default, U - per-user static route
       o - ODR, P - periodic downloaded static route

Gateway of last resort is not set is subnetted, 1 subnets
B [20/0] via, 00:00:52 is variably subnetted, 2 subnets, 2 masks
C is directly connected, FastEthernet1/0
C is directly connected, Loopback0
C is directly connected, FastEthernet0/0

The lan routers are actually switches. But I did not turned them on yet.
O.K., SITE2 router has received a route via BGP that says go get to go to

I would assume that (MPLS2) has a route that says to get to go to

Then (SITE1 router) is attached to, so it knows how to get there.

Now you need to look at the routes going back.  That is, does SITE1 router have a default route that points to or does it have some other route that points to the subnet you are on that points to  Does MPLS2 have a route that points back to your IP address.

Last, but not least, could something be configured to drop/reject ICMP packets along the way.

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