Edit I copied the question to the Astronomy site (https://astronomy.stackexchange.com/questions/36947/is-it-true-that-we-see-the-center-of-the-milky-way-for-only-half-of-the-year), as suggested in one of the comments. Thanks!.
I'm not an astronomer, please excuse my non-formal language.
Since we are located in one of the arms of the Milky way, the center of the galaxy should be in one direction from our location, while in the other direction, we stare into the "other side".
Does this mean we only see the milky way half of the year?
In the below diagram, the small circle is our year-orbit around our sun. Red dot is the earth place on day 0 of the year and the green dot is the earth location at day 180 of the year.
I know that as we are orbiting our sun, it also orbits the galaxy, but since it is so slow, it is negligible.
Is this reasonable?