“Even if a man prays, fasts and performs other commendable acts, his Greater Jihad [Inner Jihad] is reduced to meaningless ritual when his ‘baser self the incites him to evil’ has prevented him from fulfilling his Lesser Jihad [Military Jihad] … the jihad with the self is only greater than the military jihad in the sense that it is its precondition…” – Amal Saad-Ghorayeb
There is indeed both a Greater and a Lesser Jihad in Islam. No one questions that.
The thing is that they're interlinked - necessarily interlinked. There is no Greater Jihad without a Lesser Jihad and vice versa.
Also, many jihadists see the Inner Jihad (Greater Jihad) as but a means to be in the right frame of Islamic mind to carry out the Lesser Jihad (the violent jihad). Fighters need to have gone through an Inner Jihad before the violent jihad.
The other thing is the terms "Greater" and "Lesser" don't mean that one is compulsory and the other is optional; or even that one is more important than the other. Again, the Greater (Inner) Jihad is only "greater" because it's a necessary prelude to the violent jihad - which is equally necessary! The only time when the Lesser Jihad (violent jihad) is not needed from every single Muslim male is in the specific conditions when not all Muslim males are needed to fight (to win) and when it impossible for Muslims to carry out violent jihad - such as when they live in the UK and in other non-Muslim countries.
So, again, as all scholars and imams say: Muslim men who only carry out the Inner Jihad without carrying out the Lesser Jihad are a disgrace to Islam. After all, Islam, according to Muslims, is both a spiritual and a political religion. How can an Inner Jihad account for everything in such a religion when the political/social is so fundamental to Islam?