# Is it possible to use Poisson Regression for binary outcome?

First of all, I should say that I've just started to learn most of the terms I'll use in my question. Therefore I am sorry for any inconvenience I cause.

I have a dataset with 2000 instances. The dependent variable is a binary variable (either 0 or 1) and I have 3 independent varibles where one of them is categorical (Male or Female) and other two are continious (between 0 and 1). Here i a couple of examples:

     Gender       Freq_A       Freq_B Labels
1    Female 5.842289e-03 9.090465e-03      0
2      Male 3.180251e-03 4.009848e-03      1
3      Male 2.060638e-05 2.365917e-04      0
4      Male 1.930360e-02 3.868656e-03      0
5    Female 2.551375e-03 1.110913e-02      0
6    Female 3.564216e-02 3.755856e-02      1


I first apply logistic regression. However, the McFadden R2 I obtained was too small (6 e-3)

   llh       llhNull            G2      McFadden          r2ML          r2CU
-1.230380e+03 -1.239047e+03  1.733430e+01  6.995017e-03  9.583948e-03  1.281971e-02


Then, it has been told that maybe Poisson Regression might be a better fit for my case. However, all of the resources I read about Poisson regression was saying that it is a regression model best for explaning counting data. But then I found that it can also be used for binary outcome. (Source: Poisson regression for binary outcomes , link) So, I decided to apply it in my data as follows:

mydata1 <- read.csv(fname)
mydata <- mydata1[sample(nrow(mydata1)),]
train <- mydata[1:1800,]
test <- mydata[1801:2000,]
model <- glm(Labels ~ Gender + Freq_A + Freq_B,family=poisson(link='logit'),data=train)


When I do that, I get error saying:

Error in family\$linkfun(mustart) : Value 1.1 out of range (0, 1)

This error disappears if I don't use logit as a link function however I think I should use it because my output variable is binary.

So basically, I am wondering what I am doing wrong and is it possible to apply poisson regression for binary outcome data in R ?