By repeatedly stating (with a typically American attitude of pushy, presumtious ignorance) that you can't figure out how a country can stabilize another by supporting its insurgents/rebels you are loudly describing just how big of a novice you are in this subject being discussed.

I mean the concept is as old and standard as history itself.

Let me dumb it down for you:

Destabilization is not an end. It is not a final objective.
It is only a MEANS to achieve another greater end, which is
CHANGE and ultimately STABILITY under a different (more workable) order...

Now that you have been humbled. Let me give you some background info on the Horn of Africa:

Sudan's instability did not begin with Eritrean involvement,
it was there long before and had a severely adverse effect on Eritrea and many other neighbours of Sudan, ehmm not to mention on Sudan itself. Eritrean involvement does not seek
to continue destabilizing Sudan bur rather to STABILIZE Sudan, RECONCILE its difference, STRENGTHEN it, only this time under an order which is more in tune with and friendly
towards Eritrea and Eritrean interests (trade and balance of
power against the threat of ETHIOPIA).

Sudan, Somalia and Ethiopia destabilized eachother in order to ultimately win and "stabilize" eachother under the total influence and dominance of one over the other. Well in the case of Somalia it was merely to recover what it considers Somali territory (Ogaden) occupied by Ethiopia.

After Ethiopia's defeat and Eritrea's independence, Sudan hoped to take over the spoils and "stabilize" the region by exertings its influence over both countries but neither the Eritreans nor the new Ethiopian government (which Sudan considered its little puppets) complied. Both Eritrea and Ethiopia actually got along quite well since both leaders
had cooperated to overthrow the previous brutal communist dictator of Ethiopia and reverse centuries of Amhara ethnic hegemony. So Sudan went back to playing the same game with Ethiopia (destablization by way of islamic terrorism) and targetted newly independent Eritrea as well. Hence Eritrea joined Ethiopia as a junior partner against former friend Sudan. Somalia of course imploded under its own internal opposition much to the benefit of Ethiopia.

Eritrea and Ethiopia soon started fighting over the border, the economy and the level of Eritrea's true independence when Ethiopia switched to a "new" policy of recovering all of its influence over its former seacoast province with US help. Eritrea had to quickly reorganize its foreign policy as less of a partner/junior brother of Ethiopia's and one where Ethiopia became enemy no.1 once again, threatening/dwarfing its very existence.

So all Ethiopia's enemies are now Eritrea's friends. But Eritrea does not want to (cannot logically with a prominent
half-christian population) succumb to domination under an isamic force nomatter how anti-Ethiopian it is and how prepared it is to help Eritrea fight Ethiopia (this would only come at an unaffordable price). So it is taking a pragmatic risk-managing approach to dealing with Ethiopia's largely islamic and islamist enemies as allies. With Somalia there is no risk or even trend of Somali islamism spreading to Eritrea as the Somalis are not interested in spreading their rule or influence or whatever beyond their domain and are focused on recovering and reconstituting their country (which is 100% moslem anyways, so no oppressed
religious minorities to speak of). Moreover the Somali islamists are the only force who managed to peacefully unite and stabilize their country deriving their support mainly from Somalis and including all clans and groups without discrimination before facing Ethiopian agression.
So Eritrea has no problem wholeheartedly supporting them against Ethiopian agression which cynically sees a unified
Somalia as a threat and thus seeks to maintain Somalia weak,
divided and dictated to by Ethiopia. Eritrea wants a strong
and friendly Somalia to counter-balance and weaken the big
Ethiopian threat.

With Sudan, the solution is much more complicated. Eritrea
wants an equally strong and friendly Sudan for much the same
reasons, although trade is another incentive for Eritrean involvement. If you divide Sudan in two parties, one made up of the previously hostile islamic Sudanese government and the other made up of the many opposition movements all gathered under one Asmara-based umbrella, either party is too weak to totally consolidate rule over Sudan and strengthen it. So Eritrea would only be spoiling for itself and weakening Sudan by helping one side against the other.
It would also not help its budding relations with China, a major investor in Sudan's petroleum industry. So Eritrea has embarked on the feat of reconciling and uniting the Sudanese and seems to be doing quite well in that area much
to USA's and Ethiopia's dismay who see their influence has faded.