There are three major variables involve in the "perception" of a display resolution.
1) Viewing Distance
2) Screen Size
3) Resolution (and Aspect Ratio)
If a monitor has a resolution of 4K (i.e., 3840 x 2160), it will display 4K resolution, whatever its screen size or your viewing distance from it. Consequently, if a monitor has a resolution of 1080p (i.e., 1920 x 1080), it will display 1080p resolution, whatever its screen size or your viewing distance from it.
Screen size and resolution are the two factors that make up the monitor's pixel density, often abbreviated as ppi (pixels per inch), which is a measure of many pixels it can fit in one linear inch. This will determine how small or large the individual pixels of the screen is. Smaller resolutions on a larger screen size will have a less dense ppi (larger pixel size), which means the image shown on the display will appear "pixelated". Larger resolutions on a smaller screen size will have a denser ppi (smaller pixel size), which means the image will appear "sharper/smoother".
Viewing distance play a factor on the perceived image quality from the viewer. If a less dense ppi monitor is viewed at close distance, one can definitely see the jagged edges and pixels of an image. But if one views the same monitor at a significantly farther distance, one can perceive that the quality of the same image appears sharper.
This is what your father
probably meant.
At 40" and up (large screen size), the benefits of having 4K (larger resolution) is evident, as typically, you would have to position the large monitor away from you (say, more than 3 feet) to be able to see all of the screen. If the same large monitor is only 1080p (smaller resolution) and viewed at the same distance, "pixelations" will be perceived due to the less dense ppi.
Now, if you have 1080p, but you change the monitor to a smaller one (say ~20"), the ppi increases, and when viewed at a closer distance (say, 2 feet), will still appear sharp. If the same ~20" monitor is 4K (higher resolution), one may not see a noticeable difference between the less dense ppi and the denser ppi, due to the same viewing distance. To be able to get the full benefit of 4K at that screen size, one must position the monitor about 1 foot or less from your eyesight.
Note that monitors being sold that has a 29" screen size are not "1920 x 1080 (widescreen)" but rather, "2560 x 1080 (ultrawide)". 1920 x 1080 has an aspect ratio of 16:9, while 2560 x 1080 has an aspect ratio of 21:9. The 4K monitors at 3840 x 2160 also has an aspect ratio of 16:9. Therefore, when an image having a 16:9
image aspect ratio is displayed on a monitor having a 21:9
screen aspect ratio, there will be vertical black bars on both sides of the 21:9 screen.