In conveying the message of Islam to a non-Muslim, it is usually not sufficient to highlight only the positive nature of Islam. Most non-Muslims are not convinced about the truth of Islam because there are a few questions about Islam at the back of their minds that remain unanswered.
They may agree with your contentions about the positive nature of Islam. But, in the same breath, they will say - "Ah! But you are the same Muslims who marry more than one woman. You are the same people who subjugate women by keeping them behind the veil. You are fundamentalists, etc."
I personally prefer asking the non-Muslim upfront, what he feels is wrong in Islam. I prefer asking directly, what they feel is wrong in Islam with their limited knowledge, whether right or wrong and from whichever source it may be. I encourage them to be very frank and open and convince them that I can take criticism about Islam.
In the past few years of my Daawah experience, I have realized that there are barely twenty most common questions that a common non-Muslim has regarding Islam. Whenever you ask a non-Muslim, "what do you feel is wrong with Islam?", he poses five or six questions, and these questions invariably fall among the twenty most common questions.
Logical replies can convince the majority
The twenty most common questions about Islam can be answered with reason and logic. A majority of non-Muslims can be convinced with these answers. If a Muslim memorizes or simply remembers these answers, Inshallah he will be successful, if not in convincing non-Muslims about the complete truth of Islam, then at least in removing misconceptions about Islam and neutralizing the negative thinking about Islam and Muslims that the non-Muslims have. A very few non-Muslims may have counter arguments to these replies, for which further information may be required.
1. MOST COMMON QUESTIONS ASKED BY NON-MUSLIMS
2. MOST COMMON QUESTIONS ASKED BY NON-MUSLIMS WHO HAVE SOME KNOWLEDGE OF ISLAM
3. COMMON QUESTIONS ASKED BY HINDUS ABOUT ISLAM
4. COMMON QUESTIONS ASKED BY CHRISTIAN MISSIONARIES AGAINST ISLAM
5. QUERIES ON ISLAM