Yes, we do. Anyone can be saved, but not everyone is....
That does not leave a good taste in anyone's heart. But it is meant to be a pause to reflect on God's word and promises. All who seek will find.
these Doctrines of Predestination and election and such, need to be taken together to have a well rounded feel and understanding of what they are. One is no good without the other, and so we like to say that theology is a "systematic" study. You can't have the new testament without the old. In the same way these aspects of salvation are to be understood one to another. A "golden chain" if you will, where each link holds the other in succession.
We see this same type of systematic understanding in Paul's writings. Let's look at Romans 8: 28-30 just as reference of this for a bit of systematic thoughts.
28 And we know that in all things God works for the good of those who love him, who have been called according to his purpose. 29 For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters. 30 And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified
look especially at verse 30. He starts with "predestined" then explains the predestined are "called" then justified, then glorified. This may not be the best example but it's Paul explaining how one thing is dependent on another.