It's worse than that. He claims to be ex-military, but is totally unaware of even the most basic and obvious details about the strategic disposition of military forces in the Middle East.
Syria and Iran are state sponsors of terror.
Up until very recently, Lebanon has been a de facto puppet state of Syria. Even now, Syria still has a great deal of control over Lebanese policy.
Southern Lebanon (along the border with Israel) is held by Hezbollah, a terrorist organization of Palestinian refugees. Hezbollah maintains a separate government in South Lebanon, under the aegis of Syrian and Iranian diplomatic pressure on Lebanon.
Syria and Iran sponsor, supply, fund, train, and encourage terrorist groups such as Hezbollah.
Israel is not attacking Lebanon per se. Israel is attacking Hezbollah positions in southern Lebanon, because that's where they are.
Hezbollah gets its support from Syria and Iran, not from the Lebanese government.
The Lebanese government is currently powerless to stop Hezbollah, which governs a population of many thousands of Palestinians in Lebanon. The consequences of an open confrontation between the Lebanese government and Hezbollah would be devastating to that country. Lebanon would likely collapse and be annexed by Syria.
So that is why Bush is blaming Syria and Iran for instigating terrorism, even as the IDF is across the Lebanese border dealing with the terrorism that Syria and Iran have instigated.
It's a simple case of one ally tackling the difficult high-level diplomatic problem: encouraging other world leaders to join him in opposing state sponsors of terrorism (specifically, Syria and Iran), while the other ally tackles the difficult low-level military problem: shutting down the state-sponsored terrorist groups currently launching attacks on them (specifically, Syrian-sponsored Hezbollah attacks across the Lebanese border).
I guess it's true what they say: us enlisted men really are better soldiers than the officers who command us.
I bet "Colonel" Gene never really got on with his Sergeant-Major, did he?