As a history major, and someone who was always confused by this, I only ever received a valuable answer from close friends who fled Iran during the revolution in the 70s.

The main thing to remember is that 'Islam' does not equal 'Arab'. Persian culture, like many other Middle Eastern/Central Asian cultures are much older than religion (in this case, Islam). When Islam grew out of Central Arabia, it spread in many ways: trade, imperialism and other influences. After the death of the Prophet, there were 4 consecutive Islamic Caliphates (think of them as empires), which were extremely powerful and of which the territory that is now Iran was conquered by the first Rashidun Caliphate (c. 632-661 CE). This is why you often here of the Islamic world vs the 'Arab world' - which does not include Iran. This is a simple answer to the question, but there is much more going on...

The impact on Persian and Arab cultures (and many other cultures including Malay, Indian, Somali, and several North African cultures) was huge, not just in the way of religion, but in art, food, custom and of course, language.

In relation to your question on language (we all know Wikipedia is not 100% reliable, but it is a good starting place in a longer research journey); Old Persian was written in Cuneiform, which is similar to many other ancient languages. All languages have evolved immensely since those times though, so Old Persian and Modern Persian may not be mutually intelligible. This is similar to Modern vs 'Old English' or Latin. Persian, like Hindi/Urdu and several central Asian languages have loan words, phrases and grammar from Arabic; and vice-versa. The same pattern can be seen in English as a latin based language again.

Overall, I wouldn't say then 'bended' to the Arabs, I would say that they were affected by Islamic Imperialism similar to how the west was influenced by the spread of Christianity - and they maintained and adapted their culture and customs accordingly.