Mention half-brother on B1/B2 visa form, got rejected

TL;DR

I mention my half brother on the form for the B1/B2 US visa, on the interview with the consular officer she focus the interview on my brother info, his legal status (he is citizen), where he's living, etc, after that she rejected my application.

Should I mention my half-brother when reapplying? Or should I avoid that subject?

I live in Tijuana, Mexico, I want the visa mostly for travel and shopping.

Long Version

A year ago, I applied for a B1/B2 visa, on the form, under the section about family living in the US, I mentioned that my half brother lives there (he is citizen). I don't really have a strong relationship with my half-brother, he lives in Texas, I live in Tijuana, Mexico, and has been like 4 years since the last time I saw him, but still, I didn't want to hide that information on the form.

On the interview with the consular officer, she ask me 3 questions about me (what do I do for work, what did I studied and how long I been living here in Tijuana) and then ask me about my half-brother, his legal status (he's citizen), where is he living (he's in Texas), how he become citizen (he married a citizen) and when that happen, for that last question I didn't know, I told the officer that he is older than me (he's like 30 years older than me) and since I remember he's married and living in Texas.

After that the officer told me that my application was rejected, she give me a paper that said that I don't have strong ties in my country and that I can apply again.

I'm thinking on applying again, and I'm not sure if should I mention my half-brother again or not, because of the course of the interview it seems that him was the reason of the rejection, the officer didn't ask me why I want the visa (just for vacations and shopping) or anything else.

Other information, I was 26 at that time, working as Software Developer for 1 year 6 months (at that time) in the last company with a normal salary for the position.