In Writer, Inset > Picture > From File...

Select an image file and it is inserted into text as a picture frame anchored to the paragraph.

This problem also happens if you paste a copied image into the text.

Change the anchor, Right click > Anchor > As Character

Now select the image and resize by dragging the bottom right grab handle

The image resizes but the 'frame' that it sits in does not, so the text does not move up with the resized image. Placing the cursor at the start of the paragraph immediately following the picture, pressing backspace and then return makes the text correctly follow the image.